spring2008stat201exam2-version2KEY

spring2008stat201exam2-version2KEY - Stat 201 Exam 2 Spring...

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Stat 201 Exam 2 Spring 2008 Version 2 KEY Page 1 of 9 1. It was recently announced that, In the United States, 1% of U.S. adults overall are currently in prison. However, among just blacks, 7% of U.S. black adults are currently in prison. this is P(prison GIVEN black) i.e., P(Y | X) = .07 Suppose you randomly select one U.S. adult. Let X represent the event ‘the adult is black’. Let Y represent the event ‘the adult is currently in prison.’ 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) No, because 1% 7%. (ii) Yes, because 1% 7%. (iii) No, because the adult could be both black and in prison. (iv) Yes, because the adult could be both black and in prison. (v) No, because only one adult is selected. (vi) Yes, because only one adult is selected. It is certainly possible for the adult to be black, and to also be incarcerated. (b) Are the two events independent? Circle the best answer: [3 pts] (i) No, because 1% 7%. (ii) Yes, because 1% 7%. (iii) No, because the adult could be both black and in prison. (iv) Yes, because the adult could be both black and in prison. (v) No, because only one adult is selected. (vi) Yes, because only one adult is selected. With one randomly selected person, P(prison) = P(Y) = .01 but P(prison GIVEN black) = P(Y | X) = .07. Since these are not the same, ‘being black’ is not independent of ‘being in prison’. (c) Suppose that you first look at the adult’s race, but not yet at their incarceration status. If you find that the adult is black, then, given that fact, which of the following is the probability that they will also be in prison? [3 pts] The stated 7% is P(prison GIVEN black) (i) . 07 (iv) . 08 (ii) . 01 (v) . 007 (iii) zero (vi) close to 100%
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Stat 201 Exam 2 Spring 2008 Version 2 KEY Page 2 of 9 2. Suppose my brother is applying for two different college scholarships, one sponsored by the State, the other sponsored by the University. He figures his chances are as follows: 45% chance of winning the State scholarship, 60% chance of winning the University scholarship, and a 35% chance of winning both. Let S denote ‘wins the State scholarship’ Let U denote ‘wins the University 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 .35 .45 Not S .60 1 U Not U S .35 .10 .45 Not S .25 .30 .55 .60 .40 1 Of course, the table may be rotated. (b)
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spring2008stat201exam2-version2KEY - Stat 201 Exam 2 Spring...

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