{"flow": {"nodes": [{"width": 312, "height": 311, "id": "prompt-probability_questions", "type": "prompt", "data": {"prompt": "{prompt}", "n": 1, "llms": [{"key": "aa3c0f03-22bd-416e-af4d-4bf5c4278c99", "settings": {"system_msg": "You are a helpful statistician. Answer the questions with only the numerical answer rounded to 4 decimal places. Provide no explanation.", "temperature": 1, "functions": [], "function_call": "", "top_p": 1, "stop": [], "presence_penalty": 0, "frequency_penalty": 0}, "name": "GPT3.5", "emoji": "\ud83d\ude42", "model": "gpt-3.5-turbo", "base_model": "gpt-3.5-turbo", "temp": 1, "formData": {"shortname": "GPT3.5", "model": "gpt-3.5-turbo", "system_msg": "You are a helpful statistician. Answer the questions with only the numerical answer rounded to 4 decimal places. Provide no explanation.", "temperature": 1, "functions": "", "function_call": "", "top_p": 1, "stop": "", "presence_penalty": 0, "frequency_penalty": 0}}]}, "position": {"x": 448, "y": 224}, "selected": false, "positionAbsolute": {"x": 448, "y": 224}, "dragging": false}, {"width": 333, "height": 182, "id": "eval-probability_questions", "type": "evaluator", "data": {"code": "function evaluate(response) {\n\tlet ideals = JSON.parse(response.meta['Ideal']);\n\treturn ideals.some(i => response.text.startsWith(i));\n}", "language": "javascript"}, "position": {"x": 820, "y": 150}, "positionAbsolute": {"x": 820, "y": 150}}, {"width": 228, "height": 196, "id": "vis-probability_questions", "type": "vis", "data": {"input": "eval-probability_questions"}, "position": {"x": 1200, "y": 250}, "positionAbsolute": {"x": 1200, "y": 250}}, {"width": 302, "height": 260, "id": "inspect-probability_questions", "type": "inspect", "data": {"input": "prompt-probability_questions"}, "position": {"x": 820, "y": 400}, "positionAbsolute": {"x": 820, "y": 400}}, {"width": 423, "height": 417, "id": "table-probability_questions", "type": "table", "data": {"rows": [{"prompt": "A pair of fair, standard dice are rolled. What is the probability the sum of the dice is 5", "ideal": "[\"0.1111\"]"}, {"prompt": "An airplane is built to be able to fly on one engine. If the plane's two engines operate independently, and each has a 1% chance of failing in any given four-hour flight, what is the chance the plane will fail to complete a four-hour flight to Oklahoma due to engine failure?", "ideal": "[\"0.0001\"]"}, {"prompt": "A 1-inch-diameter coin is thrown on a table covered with a grid of lines two inches apart. What is the probability the coin lands in a square without touching any of the lines of the grid?", "ideal": "[\"0.2500\"]"}, {"prompt": "Of the 50 students in a certain class, 5 speak French. Two students of the class will be selected at random. Which of the following is closest to the probability that neither of the students selected will speak French?", "ideal": "[\"0.8100\"]"}, {"prompt": "Of the 10 marbles in a box, 2 are green. A person will select 2 marbles simultaneously and at random from the box. What is the probability that neither of the marbles selected will be green?", "ideal": "[\"0.6222\"]"}, {"prompt": "On a number line, there are 6 distinct points, of which 4 are positive and 2 are negative. If 2 different points are to be randomly selected, what is the probability that the 2 points selected will both be positive?", "ideal": "[\"0.4000\"]"}, {"prompt": "Of the 20 employees in a company, 5 have an MBA. If 3 employees are to be simultaneously selected at random, what is the probability that only 1 of the 3 employees selected will have an MBA?", "ideal": "[\"0.4605\"]"}, {"prompt": "Suppose that there is a coin that is weighted in such a way that each time the coin is tossed, the probability of tossing head is twice the probability of tossing a tail. What is the probability of tossing a head?", "ideal": "[\"0.6667\"]"}, {"prompt": "Suppose that there is a 6-sided die with faces numbered 1 through 6. This die is rolled twice. What is the probability that the first roll will be an odd number and the second roll will be an even number?", "ideal": "[\"0.2500\"]"}, {"prompt": "Forty-five marbles are numbered consecutively from 1 through 45. If one marble is to be drawn at random, what is the probability that the number on the selected marble will be a multiple of 5 or a multiple of 7 or a multiple of both 5 and 7 ?", "ideal": "[\"0.3111\"]"}, {"prompt": "The ratio of the probability of event X occuring to the probability of X not occuring is 5 to 9. What is the probability that event X will not occur?", "ideal": "[\"0.6429\"]"}, {"prompt": "In a set of positive integers greater than 1, the ratio of the number of prime numbers to the number of composite numbers is 3 to 7. If one number is selected at random, what is the probability that it will not be a composite number?", "ideal": "[\"0.3000\"]"}, {"prompt": "For a certain probabilistic experiment, events A and B are mutually exclusive. The probability that the event A U B (that is, the event A or B, or both) will occur is 0.6. Given that the probability of event A is 0.2, what is the probability of event B?", "ideal": "[\"0.4000\"]"}, {"prompt": "For a certain probabilistic experiment, events X and Y are independent. The probability P (X or Y) is 0.6. Given that probability P (X) = 0.5, what if the probability P (Y)?", "ideal": "[\"0.2000\"]"}, {"prompt": "Two sisters maintain that they can communicate telepathically. To test this assertion, you place the sisters in separate rooms and show sister A a series of cards. Each card is equally likely to depict either a circle or a star or a square. For each card presented to sister A, sister B writes down circle or star or square, depending on what she believes sister A to be looking at. If ten cards are shown, what is the probability that sister B correctly matches at least one?", "ideal": "[\"0.9827\"]"}, {"prompt": "An examination consists of multiple-choice questions, each having five possible answers. Suppose you are a student taking the exam. and that you reckon you have probability 0.75 of knowing the answer to any question that may be asked and that, if you do not know, you intend to guess an answer with probability 1/5 of being correct. What is the probability you will give the correct answer to a question?", "ideal": "[\"0.8000\"]"}, {"prompt": "Three babies are given a weekly health check at a clinic, and then returned randomly to their mothers. What is the probability that at least one baby goes to the right mother?", "ideal": "[\"0.6667\"]"}, {"prompt": "In a certain town, 30% of the people are Conservatives; 50% Socialists; and 20% Liberals. In this town at the last election, 65% of Conservatives voted, as did 82% of the Socialists and 50% of the Liberals. A person from the town is selected at random, and states that she voted at the last election. What is the probability that she is a Socialist?", "ideal": "[\"0.5816\"]"}, {"prompt": "A wholesaler supplies products to 10 retail stores, each of which will independently make an order on a given day with chance 0.35. What is the probability of getting exactly 2 orders?", "ideal": "[\"0.1757\"]"}, {"prompt": "A machine produces items of which 1% at random are defective. How many items can be packed in a box while keeping the chance of one or more defectives in the box to be no more than 0.5?", "ideal": "[\"68.0000\"]"}, {"prompt": "Given that 0.04% of vehicles break down when driving through a certain tunnel find the probability of no breakdowns in an hour when 2,000 vehicles enter the tunnel.", "ideal": "[\"0.4493\"]"}, {"prompt": "Given that 0.04% of vehicles break down when driving through a certain tunnel find the probability of at least 2 breakdowns in an hour when 2,000 vehicles enter the tunnel.", "ideal": "[\"0.1912\"]"}, {"prompt": "Suppose 36% of families own a dog, 30% of families own a cat, and 22% of the families that have a dog also have a cat. A family is chosen at random and found to have a cat. What is the probability they also own a dog?", "ideal": "[\"0.2640\"]"}, {"prompt": "Suppose 30% of the women in a class received an A on the test and 25% of the men received an A. The class is 60% women. Given that a person chosen at random received an A, what is the probability this person is a women?", "ideal": "[\"0.6429\"]"}, {"prompt": "Landon is 80% sure he forgot his textbook either at the Union or in Monteith. He is 40% sure that the book is at the union, and 40% sure that it is in Monteith. Given that Landon already went to Monteith and noticed his textbook is not there, what is the probability that it is at the Union?", "ideal": "[\"0.6667\"]"}, {"prompt": "An urn has 5 blue balls and 8 red balls. Each ball that is selected is returned to the urn along with an additional ball of the same color. Suppose that 3 balls are drawn in this way. What is the probability that the three balls are blue?", "ideal": "[\"0.0769\"]"}, {"prompt": "An urn has 5 blue balls and 8 red balls. Each ball that is selected is returned to the urn along with an additional ball of the same color. Suppose that 3 balls are drawn in this way. What is the probability that only 1 ball is blue?", "ideal": "[\"0.3956\"]"}, {"prompt": "Suppose you roll two standard, fair, 6-sided dice. What is the probability that the sum is at least 9 given that you rolled at least one 6?", "ideal": "[\"0.6364\"]"}, {"prompt": "A box contains 1 green ball and 1 red ball, and a second box contains 2 green and 3 red balls. First a box is chosen and afterwards a ball withdrawn from the chosen box. Both boxes are equally likely to be chosen. Given that a green ball has been withdrawn, what is the probability that the \u001cfirst box was chosen?", "ideal": "[\"0.5556\"]"}, {"prompt": "A factory production line is manufacturing bolts using three machines, A, B and C. Of the total output, machine A is responsible for 25%, machine B for 35% and machine C for the rest. It is known from previous experience with the machines that 5% of the output from machine A is defective, 4% from machine B and 2% from machine C. A bolt is chosen at random from the production line and found to be defective. What is the probability that it came from Machine A?", "ideal": "[\"0.3623\"]"}, {"prompt": "A blood test indicates the presence of Amyotrophic lateral sclerosis (ALS) 95% of the time when ALS is actually present. The same test indicates the presence of ALS 0.5% of the time when the disease is not actually present. One percent of the population actually has ALS. Calculate the probability that a person actually has ALS given that the test indicates the presence of ALS.", "ideal": "[\"0.6574\"]"}, {"prompt": "Suppose we have 3 cards identical in form except that both sides of the first card are colored red, both sides of the second card are colored black, and one side of the third card is colored red and the other side is colored black. The 3 cards are mixed up in a hat, and 1 card is randomly selected and put down on the ground. If the upper side of the chosen card is colored red, what is the probability that the other side is colored black?", "ideal": "[\"0.3333\"]"}, {"prompt": "It is estimated that 50% of emails are spam emails. Some software has been applied to filter these spam emails before they reach your inbox. A certain brand of software claims that it can detect 99% of spam emails, and the probability for a false positive (a non-spam email detected as spam) is 5%. Now if an email is detected as spam, then what is the probability that it is in fact a non-spam email?", "ideal": "[\"0.0481\"]"}, {"prompt": "Find the probability that in 10 throws of a fair die a score which is a multiple of 3 will be obtained in at least 8 of the throws.", "ideal": "[\"0.0034\"]"}, {"prompt": "Three machines E1, E2, E3 in a certain factory produce 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day\u2019s production, calculate the probability that it is defective.", "ideal": "[\"0.0425\"]"}, {"prompt": "A committee of 4 students is selected at random from a group consisting 8 boys and 4 girls. Given that there is at least one girl on the committee, calculate the probability that there are exactly 2 girls on the committee.", "ideal": "[\"0.3953\"]"}, {"prompt": "Two dice are thrown together. Let A be the event \u2018getting 6 on the first die\u2019 and B be the event \u2018getting 2 on the second die\u2019. Are the events A and B independent?", "ideal": "[\"0.0278\"]"}, {"prompt": "10% of the bulbs produced in a factory are of red colour and 2% are red and defective. If one bulb is picked up at random, determine the probability of its being defective if it is red.", "ideal": "[\"0.2000\"]"}, {"prompt": "A and B are two candidates seeking admission in a college. The probability that A is selected is 0.7 and the probability that exactly one of them is selected is 0.6. Find the probability that B is selected.", "ideal": "[\"0.2500\"]"}, {"prompt": "Suppose 100 people all toss a hat into a box and then proceed to randomly pick out a hat. What is the expected number of people to get their own hat back?", "ideal": "[\"1.0000\"]"}, {"prompt": "Let A and B be two events. Suppose the probability that neither A or B occurs is 2/3. What is the probability that one or both occur?", "ideal": "[\"0.3333\"]"}, {"prompt": "An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44. Calculate the number of blue balls in the second urn.", "ideal": "[\"4.0000\"]"}, {"prompt": "A public health researcher examines the medical records of a group of 937 men who died in 1999 and discovers that 210 of the men died from causes related to heart disease. Moreover, 312 of the 937 men had at least one parent who suffered from heart disease, and, of these 312 men, 102 died from causes related to heart disease. Calculate the probability that a man randomly selected from this group died of causes related to heart disease, given that neither of his parents suffered from heart disease.", "ideal": "[\"0.1728\"]"}, {"prompt": "Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient visits a physical therapist. Calculate the probability that a randomly chosen member of this group visits a physical therapist.", "ideal": "[\"0.4800\"]"}, {"prompt": "An insurer offers a health plan to the employees of a large company. As part of this plan, the individual employees may choose exactly two of the supplementary coverages A, B, and C, or they may choose no supplementary coverage. The proportions of the company\u2019s employees that choose coverages A, B, and C are 1/4, 1/3, and 5/12 respectively. Calculate the probability that a randomly chosen employee will choose no supplementary coverage.", "ideal": "[\"0.5000\"]"}, {"prompt": "An insurance company pays hospital claims. The number of claims that include emergency room or operating room charges is 85% of the total number of claims. The number of claims that do not include emergency room charges is 25% of the total number of claims. The occurrence of emergency room charges is independent of the occurrence of operating room charges on hospital claims. Calculate the probability that a claim submitted to the insurance company includes operating room charges.", "ideal": "[\"0.4000\"]"}, {"prompt": "Two instruments are used to measure the height, h, of a tower. The error made by the less accurate instrument is normally distributed with mean 0 and standard deviation 0.0056h. The error made by the more accurate instrument is normally distributed with mean 0 and standard deviation 0.0044h.  The errors from the two instruments are independent of each other. Calculate the probability that the average value of the two measurements is within 0.005h of the height of the tower.", "ideal": "[\"0.8384\"]"}, {"prompt": "An insurance company issues life insurance policies in three separate categories: standard, preferred, and ultra-preferred. Of the company\u2019s policyholders, 50% are standard, 40% are preferred, and 10% are ultra-preferred. Each standard policyholder has probability 0.010 of dying in the next year, each preferred policyholder has probability 0.005 of dying in the next year, and each ultra-preferred policyholder has probability 0.001 of dying in the next year. A policyholder dies in the next year. Calculate the probability that the deceased policyholder was ultra-preferred.", "ideal": "[\"0.0141\"]"}, {"prompt": "A health study tracked a group of persons for five years. At the beginning of the study, 20% were classified as heavy smokers, 30% as light smokers, and 50% as nonsmokers.  Results of the study showed that light smokers were twice as likely as nonsmokers to die during the five-year study, but only half as likely as heavy smokers.  A randomly selected participant from the study died during the five-year period.  Calculate the probability that the participant was a heavy smoker.", "ideal": "[\"0.4211\"]"}, {"prompt": "A blood test indicates the presence of a particular disease 95% of the time when the disease is actually present. The same test indicates the presence of the disease 0.5% of the time when the disease is not actually present. One percent of the population actually has the disease. Calculate the probability that a person actually has the disease given that the test indicates the presence of the disease.", "ideal": "[\"0.6574\"]"}, {"prompt": "The probability that a randomly chosen male has a blood circulation problem is 0.25. Males who have a blood circulation problem are twice as likely to be smokers as those who do not have a blood circulation problem. Calculate the probability that a male has a blood circulation problem, given that he is a smoker.", "ideal": "[\"0.4000\"]"}, {"prompt": "The number of days that elapse between the beginning of a calendar year and the moment a high-risk driver is involved in an accident is exponentially distributed. An insurance company expects that 30% of high-risk drivers will be involved in an accident during the first 50 days of a calendar year. Calculate the portion of high-risk drivers are expected to be involved in an accident during the first 80 days of a calendar year.", "ideal": "[\"0.4349\"]"}, {"prompt": "A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a 2% chance of achieving a high performance level during the coming year. The events of different employees achieving a high performance level during the coming year are mutually independent. Calculate the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high performance.", "ideal": "[\"60.0000\"]"}, {"prompt": "A large pool of adults earning their first driver\u2019s license includes 50% low-risk drivers, 30% moderate-risk drivers, and 20% high-risk drivers. Because these drivers have no prior driving record, an insurance company considers each driver to be randomly selected from the pool. This month, the insurance company writes four new policies for adults earning their first driver\u2019s license. Calculate the probability that these four will contain at least two more high-risk drivers than low-risk drivers.", "ideal": "[\"0.0488\"]"}, {"prompt": "A study is being conducted in which the health of two independent groups of ten policyholders is being monitored over a one-year period of time. Individual participants in the study drop out before the end of the study with probability 0.2 (independently of the other participants). Calculate the probability that at least nine participants complete the study in one of the two groups, but not in both groups?", "ideal": "[\"0.4692\"]"}, {"prompt": "A company takes out an insurance policy to cover accidents that occur at its manufacturing plant. The probability that one or more accidents will occur during any given month is 0.60. The numbers of accidents that occur in different months are mutually independent. Calculate the probability that there will be at least four months in which no accidents occur before the fourth month in which at least one accident occurs.", "ideal": "[\"0.2898\"]"}, {"prompt": "A piece of equipment is being insured against early failure. The time from purchase until failure of the equipment is exponentially distributed with mean 10 years. The insurance will pay an amount x if the equipment fails during the first year, and it will pay 0.5x if failure occurs during the second or third year. If failure occurs after the first three years, no payment will be made. Calculate x such that the expected payment made under this insurance is 1000.", "ideal": "[\"5644.0000\"]"}, {"prompt": "An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The amount of the benefit decreases by 1000 each successive year until it reaches 0. If the device has not failed by the beginning of any given year, the probability of failure during that year is 0.4. Calculate the expected benefit under this policy.", "ideal": "[\"2694.0000\"]"}, {"prompt": "A company buys a policy to insure its revenue in the event of major snowstorms that shut down business. The policy pays nothing for the first such snowstorm of the year and 10,000 for each one thereafter, until the end of the year. The number of major snowstorms per year that shut down business is assumed to have a Poisson distribution with mean 1.5. Calculate the expected amount paid to the company under this policy during a one-year period.", "ideal": "[\"7231.0000\"]"}, {"prompt": "A recent study indicates that the annual cost of maintaining and repairing a car in a town in Ontario averages 200 with a variance of 260. A tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e., everything is made 20% more expensive). Calculate the variance of the annual cost of maintaining and repairing a car after the tax is introduced.", "ideal": "[\"374.4000\"]"}, {"prompt": "The time to failure of a component in an electronic device has an exponential distribution with a median of four hours. Calculate the probability that the component will work without failing for at least five hours.", "ideal": "[\"0.4204\"]"}, {"prompt": "A charity receives 2025 contributions. Contributions are assumed to be mutually independent and identically distributed with mean 3125 and standard deviation 250. Calculate the approximate 90th percentile for the distribution of the total contributions received.", "ideal": "[\"6342548.0000\"]"}, {"prompt": "Claims filed under auto insurance policies follow a normal distribution with mean 19,400 and standard deviation 5,000. Calculate the probability that the average of 25 randomly selected claims exceeds 20,000.", "ideal": "[\"0.2743\"]"}, {"prompt": "An insurance company issues 1250 vision care insurance policies. The number of claims filed by a policyholder under a vision care insurance policy during one year is a Poisson random variable with mean 2. Assume the numbers of claims filed by different policyholders are mutually independent. Calculate the approximate probability that there is a total of between 2450 and 2600 claims during a one-year period?", "ideal": "[\"0.8185\"]"}, {"prompt": "A company manufactures a brand of light bulb with a lifetime in months that is normally distributed with mean 3 and variance 1. A consumer buys a number of these bulbs with the intention of replacing them successively as they burn out. The light bulbs have mutually independent lifetimes. Calculate the smallest number of bulbs to be purchased so that the succession of light bulbs produces light for at least 40 months with probability at least 0.9772.", "ideal": "[\"16.0000\"]"}, {"prompt": "A tour operator has a bus that can accommodate 20 tourists. The operator knows that tourists may not show up, so he sells 21 tickets. The probability that an individual tourist will not show up is 0.02, independent of all other tourists. Each ticket costs 50, and is non-refundable if a tourist fails to show up. If a tourist shows up and a seat is not available, the tour operator has to pay 100 (ticket cost + 50 penalty) to the tourist. Calculate the expected revenue of the tour operator.", "ideal": "[\"985.0000\"]"}, {"prompt": "A company has two electric generators. The time until failure for each generator follows an exponential distribution with mean 10. The company will begin using the second generator immediately after the first one fails. Calculate the variance of the total time that the generators produce electricity.", "ideal": "[\"200.0000\"]"}, {"prompt": "A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses. Calculate the probability that the next mattress sold is either king or queen-size.", "ideal": "[\"0.8000\"]"}, {"prompt": "Each time a hurricane arrives, a new home has a 0.4 probability of experiencing damage. The occurrences of damage in different hurricanes are mutually independent. Calculate the mode of the number of hurricanes it takes for the home to experience damage from two hurricanes.", "ideal": "[\"3.0000\"]"}, {"prompt": "From 27 pieces of luggage, an airline luggage handler damages a random sample of four. The probability that exactly one of the damaged pieces of luggage is insured is twice the probability that none of the damaged pieces are insured. Calculate the probability that exactly two of the four damaged pieces are insured.", "ideal": "[\"0.2728\"]"}, {"prompt": "Two fair dice are rolled. Let X be the absolute value of the difference between the two numbers on the dice. Calculate the probability that X < 3.", "ideal": "[\"0.6667\"]"}, {"prompt": "An urn contains four fair dice. Two have faces numbered 1, 2, 3, 4, 5, and 6; one has faces numbered 2, 2, 4, 4, 6, and 6; and one has all six faces numbered 6. One of the dice is randomly selected from the urn and rolled. The same die is rolled a second time. Calculate the probability that a 6 is rolled both times.", "ideal": "[\"0.2917\"]"}, {"prompt": "In a given region, the number of tornadoes in a one-week period is modeled by a Poisson distribution with mean 2. The numbers of tornadoes in different weeks are mutually independent. Calculate the probability that fewer than four tornadoes occur in a three-week period.", "ideal": "[\"0.1512\"]"}, {"prompt": "An electronic system contains three cooling components that operate independently. The probability of each component\u2019s failure is 0.05. The system will overheat if and only if at least two components fail. Calculate the probability that the system will overheat.", "ideal": "[\"0.0073\"]"}, {"prompt": "In a group of health insurance policyholders, 20% have high blood pressure and 30% have high cholesterol. Of the policyholders with high blood pressure, 25% have high cholesterol. A policyholder is randomly selected from the group. Calculate the probability that a policyholder has high blood pressure, given that the policyholder has high cholesterol.", "ideal": "[\"0.1667\"]"}, {"prompt": "In a group of 25 factory workers, 20 are low-risk and five are high-risk. Two of the 25 factory workers are randomly selected without replacement. Calculate the probability that exactly one of the two selected factory workers is low-risk.", "ideal": "[\"0.3333\"]"}, {"prompt": "This year, a medical insurance policyholder has probability 0.70 of having no emergency room visits, 0.85 of having no hospital stays, and 0.61 of having neither emergency room visits nor hospital stays Calculate the probability that the policyholder has at least one emergency room visit and at least one hospital stay this year.", "ideal": "[\"0.0600\"]"}, {"prompt": "A company issues auto insurance policies. There are 900 insured individuals. Fifty-four percent of them are male. If a female is randomly selected from the 900, the probability she is over 25 years old is 0.43. There are 395 total insured individuals over 25 years old. A person under 25 years old is randomly selected. Calculate the probability that the person selected is male.", "ideal": "[\"0.5327\"]"}, {"prompt": "George and Paul play a betting game. Each chooses an integer from 1 to 20 (inclusive) at random. If the two numbers differ by more than 3, George wins the bet. Otherwise, Paul wins the bet. Calculate the probability that Paul wins the bet.", "ideal": "[\"0.3200\"]"}, {"prompt": "Two fair dice are tossed. One die is red and one die is green. Calculate the probability that the sum of the numbers on the two dice is an odd number given that the number that shows on the red die is larger than the number that shows on the green die.", "ideal": "[\"0.6000\"]"}, {"prompt": "A certain brand of refrigerator has a useful life that is normally distributed with mean 10 years and standard deviation 3 years. The useful lives of these refrigerators are independent. Calculate the probability that the total useful life of two randomly selected refrigerators will exceed 1.9 times the useful life of a third randomly selected refrigerator.", "ideal": "[\"0.5561\"]"}, {"prompt": "A company has five employees on its health insurance plan. Each year, each employee independently has an 80% probability of no hospital admissions. If an employee requires one or more hospital admissions, the number of admissions is modeled by a geometric distribution with a mean of 1.50. The numbers of hospital admissions of different employees are mutually independent. Each hospital admission costs 20,000. Calculate the probability that the company\u2019s total hospital costs in a year are less than 50,000.", "ideal": "[\"0.7828\"]"}, {"prompt": "On any given day, a certain machine has either no malfunctions or exactly one malfunction. The probability of malfunction on any given day is 0.40. Machine malfunctions on different days are mutually independent. Calculate the probability that the machine has its third malfunction on the fifth day, given that the machine has not had three malfunctions in the first three days.", "ideal": "[\"0.1477\"]"}, {"prompt": "In a casino game, a gambler selects four different numbers from the first twelve positive integers. The casino then randomly draws nine numbers without replacement from the first twelve positive integers. The gambler wins the jackpot if the casino draws all four of the gambler\u2019s selected numbers. Calculate the probability that the gambler wins the jackpot.", "ideal": "[\"0.2545\"]"}, {"prompt": "Bowl I contains eight red balls and six blue balls. Bowl II is empty. Four balls are selected at random, without replacement, and transferred from bowl I to bowl II. One ball is then selected at random from bowl II. Calculate the conditional probability that two red balls and two blue balls were transferred from bowl I to bowl II, given that the ball selected from bowl II is blue.", "ideal": "[\"0.4895\"]"}, {"prompt": "A drawer contains four pairs of socks, with each pair a different color. One sock at a time is randomly drawn from the drawer until a matching pair is obtained. Calculate the probability that the maximum number of draws is required.", "ideal": "[\"0.2286\"]"}, {"prompt": "A representative of a market research firm contacts consumers by phone in order to conduct surveys. The specific consumer contacted by each phone call is randomly determined. The probability that a phone call produces a completed survey is 0.25. Calculate the probability that more than three phone calls are required to produce one completed survey.", "ideal": "[\"0.4219\"]"}, {"prompt": "A gun shop sells gunpowder. Monthly demand for gunpowder is normally distributed, averages 20 pounds, and has a standard deviation of 2 pounds. The shop manager wishes to stock gunpowder inventory at the beginning of each month so that there is only a 2% chance that the shop will run out of gunpowder (i.e., that demand will exceed inventory) in any given month. Calculate the amount of gunpowder to stock in inventory, in pounds.", "ideal": "[\"24.1080\"]"}, {"prompt": "The number of tornadoes in a given year follows a Poisson distribution with mean 3. Calculate the variance of the number of tornadoes in a year given that at least one tornado occurs.", "ideal": "[\"2.6609\"]"}, {"prompt": "Ten cards from a deck of playing cards are in a box: two diamonds, three spades, and five hearts. Two cards are randomly selected without replacement. Calculate the variance of the number of diamonds selected, given that no spade is selected.", "ideal": "[\"0.3401\"]"}, {"prompt": "A manufacturer produces computers and releases them in shipments of 100. From a shipment of 100, the probability that exactly three computers are defective is twice the probability that exactly two computers are defective. The events that different computers are defective are mutually independent. Calculate the probability that a randomly selected computer is defective.", "ideal": "[\"0.0577\"]"}, {"prompt": "In any 12-month period, the probability that a home is damaged by fire is 20% and the probability of a theft loss at a home is 30%. The occurrences of fire damage and theft loss are independent events. Calculate the probability that a randomly selected home will either be damaged by fire or will have a theft loss, but not both, during the next year.", "ideal": "[\"0.3800\"]"}, {"prompt": "The lifetime of a certain electronic device has an exponential distribution with mean 0.50. Calculate the probability that the lifetime of the device is greater than 0.70, given that it is greater than 0.40.", "ideal": "[\"0.5488\"]"}, {"prompt": "For a pregnant woman, a certain test will give the outcome \u201cnot pregnant\u201d with probability 0.10. For a non-pregnant woman, the test will give the outcome \u201cpregnant\u201d with probability 0.20. Of women who take the test, 20% are pregnant. Calculate the probability that a woman is pregnant, given her test outcome is \u201cpregnant.\u201d", "ideal": "[\"0.5294\"]"}, {"prompt": "A company is marketing an investment opportunity to four potential customers. The company believes that its probability of making a sale is 0.5 for each of the first three customers but that it is only 0.1 for the fourth customer. The customers' purchases are independent of one another. Calculate the probability that at most two customers purchase the investment.", "ideal": "[\"0.8375\"]"}, {"prompt": "An experiment consists of tossing three fair coins and is deemed a success if the result is three heads or three tails. The experiment is repeated until a success occurs. Calculate the probability that it takes exactly three experiments to obtain a success.", "ideal": "[\"0.1406\"]"}, {"prompt": "Data on a certain pregnancy test show that a pregnant woman will test negative or not pregnant 10% of the time, while a non-pregnant woman will test positive 20% of the time. Thirty percent of the women who take the test are pregnant. Calculate the probability that a woman is pregnant given that her test outcome is positive.", "ideal": "[\"0.6585\"]"}, {"prompt": "A company is marketing an investment opportunity to four potential customers. The company believes that its probability of making a sale is 0.7 for each of the first three customers but that it is only 0.2 for the fourth customer. The customers' purchases are independent of one another. Calculate the probability that at most two customers purchase the investment.", "ideal": "[\"0.5688\"]"}, {"prompt": "An investor invests 100 dollars in a stock. Each month, the investment has probability 0.5 of increasing by 1.10 dollars and probability 0.5 of decreasing by 0.90 dollars. The changes in price in different months are mutually independent. Calculate the probability that the investment has a value greater than 91 dollars at the end of month 100.", "ideal": "[\"0.9713\"]"}, {"prompt": "A car and a bus arrive at a railroad crossing at times independently and uniformly distributed between 7:15 and 7:30. A train arrives at the crossing at 7:20 and halts traffic at the crossing for five minutes. Calculate the probability that the waiting time of the car or the bus at the crossing exceeds three minutes.", "ideal": "[\"0.2489\"]"}], "columns": [{"key": "prompt", "header": "Prompt"}, {"key": "ideal", "header": "Ideal"}]}, "position": {"x": -16, "y": 160}, "selected": false, "positionAbsolute": {"x": -16, "y": 160}, "dragging": false}], "edges": [{"source": "prompt-probability_questions", "sourceHandle": "prompt", "target": "eval-probability_questions", "targetHandle": "responseBatch", "interactionWidth": 100, "markerEnd": {"type": "arrow", "width": "22px", "height": "22px"}, "id": "reactflow__edge-prompt-1686756357355prompt-eval-1686756357355responseBatch"}, {"source": "prompt-probability_questions", "sourceHandle": "prompt", "target": "inspect-probability_questions", "targetHandle": "input", "interactionWidth": 100, "markerEnd": {"type": "arrow", "width": "22px", "height": "22px"}, "id": "reactflow__edge-prompt-1686756357355prompt-inspect-1686756357355input"}, {"source": "eval-probability_questions", "sourceHandle": "output", "target": "vis-probability_questions", "targetHandle": "input", "interactionWidth": 100, "markerEnd": {"type": "arrow", "width": "22px", "height": "22px"}, "id": "reactflow__edge-eval-1686756357355output-vis-1686756357355input"}, {"source": "table-probability_questions", "sourceHandle": "Prompt", "target": "prompt-probability_questions", "targetHandle": "prompt", "interactionWidth": 100, "markerEnd": {"type": "arrow", "width": "22px", "height": "22px"}, "id": "reactflow__edge-table-1686756385002Prompt-prompt-1686756357355prompt"}], "viewport": {"x": 144, "y": 37, "zoom": 1}}, "cache": {"eval-1686756357355.json": {}, "inspect-1686756357355.json": {}, "prompt-1686756357355.json": {}, "table-1686756385002.json": {}, "vis-1686756357355.json": {}}}