Prove that P(A \cap B|A) \ge P(A \cap B |A \cup B). They wanted to know what proportion of employees would use an office creche if made available. This season, the probability that the Yankees will win a game is 0.44 and the probability that the Yankees will score 5 or more runs in a game is 0.6. However, about 27% of the people under 65 years old get the flu each year... An auditing firm has developed a set of criteria for determining whether a particular account (and its balance) is in error. On 40% of his calls, there is no answer or the line is busy. Roll a pair of dice. ouY choose a door. If you're seeing this message, it means we're having trouble loading external resources on our website. You are told that P(A) = 0.25, P(B) = 0.35 and P(A and B) = 0.15. Suppose that E and F are two events and that P(E and F) = 0.1 and P(E) = 0.4, what is P (F|E)? an even number, given that the number rolled was 5. We have a money box with 12 $25 tickets, 12 $5 tickets, and 11 $1 tickets. If a woman takes an early pregnancy test, she will either test positive, meaning that the test says she is pregnant, or test negative, meaning that the test says she is not pregnant. Let A be the event that the employee chosen is a female, and B the event that the employee holds a managerial position. The formal way to revise probabilities based on new information is to use: a. complementary probabilities b. common sense probabilities c. conditional probabilities d. unilateral probabilities. In a group of four hatchlings that have made it to the sea, what is the probabi... One thousand nine hundred eighty-five randomly selected adults were asked if they are in favor of or against cloning. Assume P(C) = 0.2, P(D) = 0.6, and P(C|D) = 0.1. What percent of those who passed the maths test also passed the science test? This is the currently selected item. There are 6 women and 5 men on a committee. Learn conditional probability at your own pace. Of the drivers who stop at a gas station, 93% purchase gasoline, and 5% purchase both gasoline and oil. Otherwise he... Raji answers each of two multiple choice questions at random. Given a black card, what is the probability that it is a spade? if the mammograms are 0.91 accurate detecting canc... Find the indicated probability. The percent of students taking math is 30%. Suppose two cards are dealt from a deck of 52. Of these, 21 are sophomores, 23 are social science majors, and 7 are neither. There is a probability of 0.64 that we will elect a Republican president in the year 2016. If two cards are drawn without replacement from a deck, Find the probability that the second card is a spade, given that the first card was a spade. In a college graduating class of 100 students, 54 studied Mathematics, 69 studied History, and 35 studied both History and Mathematics. Everest every year. If the firm loses project A, the prob... What is conditional probability? If there is no recession the probability of reduc... For two events, A and B, P(A) = 0.2, P(B) = 0.5 and P(A|B) = 0.2. a. Round answer to three decimal places. Based on the data in the table below, what is the probability that a customer who sometimes buys generic products visits the store infrequently? The sum is 8 given that the numbers match? A. a... A survey showed that 23 % of college students read newspapers on a regular basis and that 83 % of college students regularly watch the news on TV. A student is selected at random from the class. The chance that an individual will fail the bar exam is 0.4. P(A) = 0.5 Two balls are drawn without replacement. If somebody tests positive for that disease, is... Forty percent of the Northwestern faculty teach online classes and 25 % of the faculty teach part time. Suppose that E and F are two events and that P(E and F) = 0.56 and P(E) = 0.8. Given a standard deck of cards, what is the probability of drawing a face card, given that it is a red card? Box A contains two yellow balls and four green balls. Keep all intermed... Let S be the event that a randomly chosen female aged 18-24 is a smoker. Suppose also that 2% of all adults both are obese and suffer from diabetes. Suppose that 100 former customers of an online retailer were asked in an email survey whether they preferred free 3-day shipping or whether they preferred overnight shipping for $4.99. What is the probability that a car chosen at random is red? The option to buy extended warranties is commonplace with most electronics purchases. One bag contains two times as many white balls as black balls. In the below example, there are two possible events that can occur. Assume that two fair dice are rolled. In a certain college class, 55% of the admitted students were in the top 10% of their high school class, 30% were in the next 10%, and the remaining 15% were below the top 20%. Suppose your friends have the following ice cream flavor preferences: 70% of your friends like chocolate (C). However, when they attempt the exam the second time, the chance of passing increases to 0.8. Find P(A|B) when P(A B) = 1/8 and A and B are independent. We take a random ball from the first jar and throw it into the second jar and draw a random... 99 percent sensitive and 95 percent specific with 2 percent of employees on drugs. A test is used to determine whether a person is infected. Find the probability that C and D both happen. Calculate : P( greater than 1 car | 2 to 4 kids) = [{Blank}]. What is P(F|E)? The table shows the results of a survey of college students' first class of the day. Of all the vehicles, 32% are red cars. What is the probability that the other child is also a girl? The probability that automobile sales will increase next month (A) is estimated to be 0.40. If 40 tickets are sold and 2 prizes are to be awarded, find the probability that one person will win both prizes if that person buys exactly 2 tickets. find the probabil... A doctor gives a patient a 60% chance of surviving bypass surgery after a heart attack. C = at least one of the dice shows a 1. Given P(A and B) = 0.34, P(B) = 0.62, P(\frac{B}{A}) = 0.94, what is P(A)? Consider the rolling of 2 six-sided fair dice, find the conditional probability P(first dice =3 | sum of two dice = 7). The probability that a car has a certain factory defect is 8/25. Suppose there is a 0.21 probability your roommate will forget to mail it. An experiment is performed one time as follows. What is the probabili... An automobile manufacturing plant produced 29 vehicles today: 9 were sedans, 10 were vans, and 10. A hand is chosen at random and the coin is flipped. If four balls are selected simultaneously and at random and the color is noted, find the probability that 1. Consider a situation along the line of that in United States v. Carroll Towing Co., the case that led L. Hand to express what is now known as the "Hand Rule." Suppose that a certain college class contains 64 students. Get help with your Conditional probability homework. Find p(a|b). Some of the patients are on feeding tubes while others are on IVs only. The Athletic Director gives a drug test which registers correctly as positive in 84% of the cases where the drug is present and cor... A box contains 13 black and 11 white balls. About 53% of Americans use social media and other websites to voice their opinions about television programs. Given the following partial relative frequency table. (a) What is P ( A | C )? Box 2 contains 2000 light bulbs of which 5% are defective. What P(F|E)? Find P(A | B) (to 4 decimals). Define the events A = {a, b, c}, B = {c, d}, and C = {d}. Determine the probability that a random sample of 4 managers contains: a. A subcommittee of three people is selected at random. If a single fair die is rolled, Find the probability of the following result. The probability of an economic decline in the year 2016 is 0.23. Conditional probability and independence. The probability that a man watches the show, given that... A bicycle factory runs two assembly lines, A and B . Find P(A|B) when P(A) = 0.3 and A and B are independent. BROWSE BY DIFFICULTY. (b) If P(A | B) = 0.7, compute P(A and B). Sort by: Top Voted. Suppose that i... Henry Chow is a stockbroker working for Merrill Lynch. We are interested in the children's genders. Given the contingency table shown here, find the probability that a mother with some college smoked during pregnancy. A double, given that the sum was 11. Of the remaining customers who use other forms of payment, 25% use the store's credit card for payment. A conditional probability is the probability of an event, given some other event has already occurred. If P(A|B) = .4 , then a. P(B|A) = .6 b. P(A) ast P(B) = .4 c. P(A) / P(B) = .4 d. None of the alternatives is correct. (b) If P(A | B) = 0.9 , compute P(A and B) . Let A be the event that the sum of the dice is an even number. Let (\Omega, \mathbb{P})=([0,1], \lambda) where \mathbb{P}([a,b])=b-a. Explain with an example. Of this 51%, about 7 out of 10 strongly oppose the casino. Use the contingency table below to find the following probabilities. Hot Network Questions To whom it may concern Why is it "she really done me"? This tim... An urn contains 3 red balls and 2 white balls. There are five people coming to a "party" on a particular episode of a tv show. The probability of selecting a green ball and then a yellow ball is 0.28. A recent question about probability has ties to Venn diagrams, tables, and Bayes’ Theorem. if the pt survives the surgery, then the patient has a 40% chance that the heart damage will heal. As depicted by above diagram, sample space is given by S and there are two events A and B. Find the probability that Janice develops lung cancer, given that she smokes. It is estimated that 92 % of senior citizens suffer from sleep disorders and 8 % suffer from anxiety. What is the probability that one ball selected at random will be red given that it is not white? Let B be the event that a number is less than 11. Their run plays gain yardage 98% of the time. In a random selection,... A department store finds that 20% of its customers pay by cash. = 62.5%. 25% of the students passed both the tests and 40% of the students passed the maths test. It is depicted by P(A|B). Select your answer by clicking on its button. Of these, 23 are freshmen, 28 are history majors, and 8 are neither. Suppose that E and F are two events, and that P(E) = 0.1 and P(F|E) = 0.2. In a box, there are 8 red, 4 green and 6 white balls. In cars with ABS brakes, faults occasionally occur with the wheel sensors, and a warning light is illuminated. Find the probability that the coin chosen... Mr. DiNardo's literature class has 101 students, classified by academic year and gender, as illustrated in the table. 0.525 c. 0.571 d. 0.120. What is the probab... Eighteen out of twenty managers at a large discount auto chain have college degrees. Our goal is then to determine the conditional probability Pr(A | B). According to a study published in a reputable science magazine, about 6 women in 100,000 have cervical cancer (C), so P(C) - 0.00006. Find A|B 2. Based on data from a statistical abstract, only about 20% of senior citizens (65 years old or older) get the flu each year. Courses. Services, Working Scholars® Bringing Tuition-Free College to the Community. In a community with a population of 10,000 people, the prevalence of a certain disease is 5%. Round your answer to three decimal places. Suppose that 3% of all adults suffer from diabetes and that 29% of all adults are obese. We roll two dice (all 36 outcomes are equiprobable). In a standard deck of cards, the jack, queen, and king are "face cards." There is a 45% chance of high winds if it rains and a 15% chance of high winds if it does not rain. If two events a and b are independent and you know that p(a) = 0.40, what is the value of p(a | b)? 0.0685 b. Leave a Reply Cancel reply. Determine the prob... An instructor is teaching two sections (classes) of Calculus. Solution: A total of 8% purchase oil. The probability of a recession next year is 0.4. Of the people who fished at Mountain View Park today, 32 had a license, and 8 did not. According to a recent report, 60% of U.S. college graduates cannot find a full time job in their chosen profession. a. If the event of interest is A and the event B is known or assumed to have occurred, “the conditional probability of A given B”, or “the probability of A under the condition B”. Let S be a sample space and E and F be events associated with S. Suppose that Pr(E) = 1 / 3 , Pr(F) = 5 / {12}, and Pr(E U F) = 2 / 3. You roll two dice. Suppose that 4 % of all adults suffer from diabetes and that 29 % of all adults are obese. P(H = 0)? The box contains an additional 20 "dummy" tickets with no value. According to a survey, 50% of the residents of a city oppose a downtown casino. What is the probabi... You roll a fair six-sided die and don't look at it. Now suppose that we dra... Find the joint probability of AA and BB for the following. The events are usually written as P(A|B), or sometimes P B(A). Suppose also that 1% of all adults both are obese and suffer from diabetes. The concept is one of the quintessential concepts in probability theory Total Probability Rule The Total Probability Rule (also known as the law of total probability) is a fundamental rule in statistics relating to conditional and marginal. If e and f are mutually exclusive events and p(e) = 0.15 while p(f) = 0.71, find p(e | f). The probability that she studies is 0.9. The table shows the number of male and female students enrolled in nursing at a particular university. Some of the patients are on feeding tubes while others are on IVs only. Find the unconditional mean and variance o... A university found it could classify its students into one of the three general categories: morning students (44%), afternoon students (31%), and evening students. What is the probability of getting at least 4 heads, given that a tosser got at least 2 heads? Historically, 60% of the batteries are from manufacturer 1, and 90% of there batteries last for over 40 hours. The percentage of adult users on the internet who use facebook has increased over time. HARD. In a class of students, the following data table summarizes how many students have a brother or a sister. What is P(B)? Answer choices have been rounded to the nearest percent. a) P(A) = 0.36 and P(B|A) = 0.87 b) P(B) = 0.53 and P(A|B) = 0.22. Participants in a study of a new medication received either medication A or a placebo. There are 2 urns. Tuberculosis (TB) testing most medical tests are not completely accurate. Conditional probability Explained Visually. Important questions on Conditional Probability. MEDIUM. = P(B|A) Find the probability of randomly selecting a number between 1 and 1000 (including both ends) which is divisible by: a. Given the standard deck of cards, what is the probability of drawing a red card, given that it is a face card? The probability that a car has a certain factory defect and needs an oil change is 7/50. A recent news article noted that most people who win the U.S. presidential election tend to do so on their first try; in fact, in the past century, this is true in 75% of cases. Find P[B]. 3. b. Sciences, Culinary Arts and Personal What are the probabilities: 1. = Condition probability of B given A Conditional Probability Definition We use a simple example to explain conditional probabilities. Of the 26 males, 16 are white, and 10 are spotted. In a factory, 85% of female workers are not union members, while only 15% of male workers are not union members. Suppose that 4 % of all adults suffer from diabetes and that 30% of all adults are obese. Otherwise, explain what information is needed. There are two coins in a box; one coin is a fair coin, and the other is a biased coin that comes up heads 75 percent of the time. 0.510 B. One class, however, consists of students who have also t... What is the P(male vert already took stats class)? The probability that stock A will rise in price is 0.50, and the probability that stock B will rise in price is 0.50. The screening indicated that 92.3% of them had a negative test result. A medical firm has a new test to detect Urticaria. a) Find the probability that a... How will marketers change their social media use in the near future? Suppose that 4% of all adults suffer from diabetes and that 30% of all adults are obese. Conditional Probability Questions and Answers (1,205 questions and answers). Of the female students, 200 are smokers and 300 are non-smokers. Jerry calls people and tries to sell them an auto insurance policy. A letter is known to have come either from TATANAGAR or from CALCUTTA. The probability of selecting a green ball on the first draw is 0.5. A student is selected at random from the class (a) What is... Let A be the event that student is enrolled in an Accounting course and S be the event that student is enrolled in a Statistics course. 0.1080711 c. 0.3242754 d. 0.5642458 e. 0.8709677. Given the following partial relative frequency table: | |Republican| Democrat| Independent |Male| 0.194| 0.135| 0.166 |Female| 0.141| 0.187| ? Find the probability that a randomly selected resident opposes the casino and strongly op... Is this company a good place to work ? If the firm wins project A, the probability of winning project B is 0.6. Let A be the event that the product of the two rolls is at most 5, and B be the event that the first one is an even number. What the probability that an employee doesn't use drugs assuming the test came back negative? = 0.625 If a d... A car gets involved in an accident 80% of the time if it is defective. Consider rolling a fair 6-faced die twice. Researchers carried out a study on small children, where they pretended to go shopping together and. Find... Depression is a mood disorder which is usually associated with significant mental health problems. According to the given, Determine P(B/A). If two events a and b are independent and you know that P(a)=0.90, what is the value of P(a|b)? The formula for conditional probability for both the conditions i.e. If a and b are independent events, p(a)=0.15, and p(b)=0.63, what is p(b|a)? He has probability 0.10 of buying a fake for an original but never rejects an original as a fake, What is the (conditional) probability the painting he purchases is an original? There are three doors, behind one a nice car, behind each of the other two a goat eating a bale of straw. = 0.56, Amazing but still i would like to have more examples, Your email address will not be published. The following are her predictions for the real estate market in 2016. (a) compute p(a and b). The probability that a patient visits a physical thera... A fair six-sided die is thrown twice. The data represent the number of driving fatalities for a certain area by age for male and female drivers. What is the probability that the total of two dice will be greater than 9, given that the first die is a 5? Two balls are drawn from the box (without replacement) and it was noted that the second ball is black. Consider rolling a fair 6-faced die twice. It is estimated that 67 percent of all students take economics, 73 percent of all students take math, and 58 percent of all students take both. What is P(F|E)? He knows from past experience that there is a 70% chance that his new client will want to include U.S. equity in her portfolio and a 50% chanc... A bicycle factory runs two assembly lines, A and B. What is the probability that a randomly chosen applicant has a graduate degree, given that they are f... A stable has all American Quarter Horses. = P(A ⋂ B)/P(A) Earn Transferable Credit & Get your Degree. Given P(A) = 0.4 and P(B) = 0.8. Collecting data on traffic accident fatalities, the National Highway Traffic Safety Administration has found that 47.9% of the victims have 0.0% blood alcohol content (BAC); 11.1% of the victims ha... A commission studying employment in towns hard hit by a recession has collected data on which the following questions have been based. You are going to remove the batteries to find the 2 that are defective. Of all the vehicles, 85% are cars. In a large hospital, twenty-five percent of the employees are medical professionals, fifteen percent are social workers, and the rest are administrators. Historically, they know that of balances that were in error, 75 percent... Use the data in the following table that shows results from a polygraph (lie detector). Given that P(A AND B) = 0.10 and P(A|B) = 0.40, what is P(B)? What is the probability that the number is 4, given that it is known to be an even number? If a car is involved in an accident, wh... Thirty percent of the managers in a certain company have MBA degrees as well as professional training. a. Assume breast cancer affects 0.005 percent of the female population between 45 and 55 years of age.