Probability Practice Problem (Collected By: Avash Bhattarai)1. At a university with 1,000 business majors, there are 200 business students who are enrolled in

an introductory statistics course. Of these 200 students, 50 are also enrolled in an introductory accounting course. There are an additional 250 business students who are enrolled in accounting but are not enrolled in statistics. If a business student is selected at random, what is the probability that

a. The student is either enrolled in accounting or statistics? ANSWER: 0.45 b. The student is enrolled in accounting? ANSWER: 0.30 c. The student is enrolled in statistics? ANSWER: 0.20 d. The student is enrolled in both statistics and accounting? ANSWER: 0.05 e. Suppose it is found that the student is enrolled in statistics, what is the probability that

the student is also enrolled in accounting? ANSWER: 0.25 f. Suppose it is found that the student is enrolled in accounting, what is the probability that

the student is also enrolled in statistics? ANSWER: 50/300

2. A survey is taken among customers of a fast-food restaurant to determine preference for hamburger or chicken. Of 200 respondents selected, 75 were children and 125 were adults. 120 preferred hamburger and 80 preferred chicken. 55 of the children preferred hamburger. What is the probability that a randomly selected individual is

a) An adult or a child? ANSWER: 1.00 b) A child and prefers chicken? ANSWER: 0.10 c) An adult and prefers chicken? ANSWER: 0.30 d) A child or prefers hamburger? ANSWER: 0.70 e) Assume we know the person is a child. What is the probability that this individual

prefers hamburger? ANSWER: 55/75 f) Assume we know that a person has ordered chicken. What is the probability that this

individual is an adult? ANSWER: 0.75 g) Assume we know that a person has ordered hamburger. What is the probability that this

individual is a child? ANSWER: 55/120

3. Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine. 70% said that they preferred beer. 60% of the patrons were male. 80% of the males preferred beer. What is the probability thata) A randomly selected patron prefers wine? ANSWER: 0.30 b) A randomly selected patron is a female? ANSWER: 0.40 c) A randomly selected patron is a female who prefers wine? ANSWER: 0.18 d) A randomly selected patron is a female who prefers beer? ANSWER: 0.22 e) Suppose a randomly selected patron prefers wine. What is the probability that the patron is

a male? ANSWER: 0.40 f) Suppose a randomly selected patron prefers beer. What is the probability that the patron is a

male? ANSWER: 0.69 g) Suppose a randomly selected patron is a female. What is the probability that the patron

prefers beer? ANSWER: 0.55

4. At a Texas college, 60% of the students are from the southern part of the state, 30% are from the northern part of the state, and the remaining 10% are from out of state. All students must take and pass an Entry Level Math (ELM) test. 60% of the southerners have passed the ELM, 70% of the northerners have passed the ELM, and 90% of the out-of-states have passed the ELM. What is the probability that

a) A randomly selected student is someone from northern Texas who has not passed the ELM? ANSWER: 0.09

b) A randomly selected student has passed the ELM? ANSWER: 0.66 c) A randomly selected student is not from southern Texas and has not passed the ELM?

ANSWER: 0.10 d) If a randomly selected student has passed the ELM, what is the probability that the

student is from out of state? ANSWER: 0.136

e) If a randomly selected student has not passed the ELM, what is the probability that the student is from southern Texas? ANSWER: 0.706

f) If a randomly selected student has not passed the ELM, what is the probability that the student is not from northern Texas? ANSWER: 0.735

g) If a randomly selected student is not from southern Texas, what is the probability that the student has not passed the ELM? ANSWER: 0.25

h) If a randomly selected student is not from out of state, what is the probability that the student has passed the ELM? ANSWER: 0.633

5. According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $25K is 80%. Of the households surveyed, 60% had incomes over $25K and 70% had 2 cars. What is the probability that a) The residents of a household own 2 cars and have an income over $25K a year? b) The residents of a household do not own 2 cars and have an income over $25K a year? c) The residents of a household own 2 cars and have an income up to $25K a year? d) Annual household income is over $25K if the residents of a household own 2 cars? e) Annual household income is over $25K if the residents of a household do not own 2 cars? f) The residents do not own 2 cars if annual household income is not over $25K?

ANSWER: (a) 0.48; (b) 0.12; (c) 0.22; (d) 0.6857; (e) 0.40; (f) 0.456. It is known from experience that in a certain industry 60% of all labor-management disputes are

over wages, 15% are over working conditions, and 25% are over fringe issues. Also 45% of the disputes over wages are resolved without strikes, 70% of the disputes over working conditions are resolved without strikes, and 40% of the disputes over fringe issues are resolved without strikes. What is the probability that if a labor-management disputes in this industry is resolved without a strike, it was over wages? ANSWER: 0.56842

7. A public interest group was planning to make a court challenge to auto insurance rates in one of three cities: Atlanta, Baltimore, and Cleveland. The probability that it would choose Atlanta was 0.40; Baltimore 0.35; and Cleveland 0.25. The group also knows that it had a 60% chance of a favorable ruling if it chose Baltimore, 45% if it chose Atlanta, and 35% if it chose Cleveland. If the group did receive a favorable ruling, which city did it most likely choose? ANSWER: Baltimore

8. An economist believes that during periods of high economic growth, the U.S. dollar appreciates with probability 0.70; in periods of moderate economic growth, the dollar appreciates with probability 0.40; and during periods of low economic growth, the dollar appreciates with probability 0.20. During any period of time, the probability of high economic growth is 0.30, the probability of moderate economic growth is 0.50, and the probability of low economic growth is 0.20. Suppose the dollar has been appreciating during the present period. What is the probability we are experiencing a period of high economic growth? ANSWER: 0.467

9. A drug manufacturer believes there is 0.95 chances that the Food and Drug Administration (FDA) will approve a new drug the company plans to distribute if the results of current testing show that the drug causes no side effects. The manufacturer further believes there is a 0.50 probability that the FDA will approve the drug if the test shows that the drug does cause side effects. A physician working for the drug manufacturer believes there is a 0.20 probability that tests will show that the drug causes side effects. What is the probability that the drug will be approved by the FDA? If the drug will be approved by the FDA, what is the probability that it really causes no side effects? ANSWER: 0.86, 0.8837

10. An import-export firm has a 0.45 chance of concluding a deal to export agricultural equipment to a developing nation if a major competitor does not bid for the contract, and a 0.25 probability of concluding the deal if the competitor does bid for it. It is estimated that the competitor will submit the bid for the contract with probability 0.40. What is the probability of getting the deal? Given that the firm has just concluded the deal, what is the probability that the competitor does not bid for the contract? ANSWER: 0.37, 0.7297

11. An oil explorer orders seismic tests to determine whether oil is likely to be found in a certain drilling area. The seismic tests have a known reliability. When oil does exist in the testing area, the test will indicate so 85% of the time; when oil does not exist in the test area, 10% of the time the test will erroneously indicate that it does exist. The explorer believes that the probability of existence of an oil deposit in the test area is 0.4. If test is conducted and indicates the presence of oil, what is the probability that an oil deposit really exists? ANSWER: 0.85