1. A group of thirty-six people is selected at random. What is the probability that at least two of them will have the same birthday? (Round your answer to four decimal places.)
• You order sixteen burritos to go from a Mexican restaurant, nine with hot peppers and seven without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability of the given event. (Round your answer to three decimal places. All have hot peppers.
• Four hundred people apply for three jobs. One hundred twenty of the applicants are women.

(a) If three people are selected at random, what is the probability that all are women? (Round your answer to six decimal places.)

(b) If three people are selected at random, what is the probability that two are women? (Round your answer to six decimal places.)

(c) If three people are selected at random, what is the probability that one is a woman? (Round your answer to six decimal places.)

(d) If three people are selected at random, what is the probability that none is a woman? (Round your answer to six decimal places.)

(e) If you were an applicant, and the three selected people were not of your gender, should the above probabilities have an impact on your situation? Why? Choose one.

-The probabilities do not indicate presence or absence of gender discrimination. For the employer to choose the most appropriate person for the job means that not all events are equally likely.

-Yes, the probabilities indicate the presence of gender discrimination.

-No, the probabilities do not indicate the presence of gender discrimination because in the hiring process all outcomes are equally likely.

• On the basis of his sale records, a salesman knows that his weekly commissions have the probabilities shown below.

Find the salesman’s expected commission.

\$____________

• Of all students at the University of Metropolis, the proportions taking certain numbers of units are as shown in the table below.

Find the expected number of units that a student at U.M. takes. (Enter your answer to two decimal places.)
_____ units

• You are on a TV show. You have been asked to either play a dice game five times or accept a \$50 bill. The dice game works like this:

• If you roll a 1, 2, or 3, you win \$50.
• If you roll a 4 or 5, you lose \$25.
• If you roll a 6 you lose \$70.

Should you play the game? Use expected values and decision theory to justify your answer. Choose one.

-Yes, you should play because the expected value is positive.

-Yes, you should play because the expected value is more than \$50.

-No, you should not play because the expected value is negative.

-No, you should not play because the expected value is less than \$50.

• Few students manage to complete their schooling without taking a standardized admissions test such as the Scholastic Achievement Test, or SAT (used for admission to college); the Law School Admissions Test, or LSAT; and the Graduate Record Exam, or GRE (used for admission to graduate school). Sometimes, these multiple-choice tests discourage guessing by subtracting points for wrong answers. In particular, a correct answer will be worth +1 point, and an incorrect answer on a question with five listed answers (a through e) will be worth -1/4 point.

(a) Find the expected value of a random guess.
________

(b) Find the expected value of eliminating one answer and guessing among the remaining four possible answers. (Enter an exact number as an integer, fraction, or decimal.)
________

(c) Find the expected value of eliminating three answers and guessing between the remaining two possible answers. (Enter an exact number as an integer, fraction, or decimal.)
________

(d) Use decision theory and your answers to parts (a), (b), and (c) to create a guessing strategy for standardized tests such as the SAT. Choose one.

-If you can eliminate one or more answers, guessing is a winning strategy.

-Random guessing is a winning strategy.

-There is no winning strategy for guessing.

-If you can eliminate no less than three answers, guessing is a winning strategy.

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