spring2008stat201exam2-version3KEY

# spring2008stat201exam2-version3KEY - Stat 201 Exam 2 Spring...

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Stat 201 Exam 2 Spring 2008 Version 3 KEY Page 1 of 9 1. In the United States, 12% of the population is black; while in Britain, only 1 . 6% of the population is black. this is P(X) this is P(Y) Suppose you randomly select two people: One from the U.S., and one from Britain. Let X represent the event ‘the American is black’. Let Y represent the event ‘the Brit is black.’ Remark: This exercise was anticipated by exercises 1 and 2 on the practice exam; it is just like scenario 3 of lab 6 and exercise 1 of lecture 12; the ideas were covered in various exercises of homework 6, and throughout lectures 10, 11, and 12. (a) Are the two events disjoint? Circle the best answer: [3 pts] (i) Yes, because 12% 1 . 6% (ii) No, because 12% 1 . 6% (iii) Yes, because both people could be black. (iv) No, because both people could be black. (v) Yes, because each person is selected from a different country. (vi) No, because each person is selected from a different country. (b) Are the two events independent? Circle the best answer: [3 pts] (i) Yes, because 12% 1 . 6% (ii) No, because 12% 1 . 6% (iii) Yes, because both people could be black. (iv) No, because both people could be black. (v) Yes, because each person is selected from a different country. (vi) No, because each person is selected from a different country. Regardless of what you select from the U.S., the chance of getting a black Brit is still 1.6% Symbolically, P(Y given X) = P(Y) (c) Suppose that you first look at the American, but not yet at the Brit. If you find that the American is black, then, given that fact, which of the following is most reasonably the probability that the Brit will then be black? [3 pts] P(Y given X) = P(Y), because the events are independent (i) zero (iv) . 136 (ii) . 12 (v) . 13408 (iii) . 016 (vi) close to 100%

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Stat 201 Exam 2 Spring 2008 Version 3 KEY Page 2 of 9 2. Suppose my brother is applying for two different college scholarships, one sponsored by the University, the other sponsored by the State. He figures his chances are as follows: 70% chance of winning the University scholarship, 75% chance of winning the State scholarship, and a 65% chance of winning both. Let U denote ‘wins the University scholarship’. Let S denote ‘wins the State scholarship’ (a) Please make a joint probability table representing this scenario, and fill-in all the probabilities. [6 pts] The information gives the following three values: U Not U S .65 .75 Not S .70 1 U Not U S .65 .10 .75 Not S .05 .20 .25 .70 .30 1 Of course, the table may be rotated. (b)
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## This note was uploaded on 02/01/2009 for the course STAT 36-201 taught by Professor Gordon during the Fall '08 term at Carnegie Mellon.

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spring2008stat201exam2-version3KEY - Stat 201 Exam 2 Spring...

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