ch12 - Chapter 12 Solutions 12.1 It is unlikely that these...

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Chapter 12 Solutions 12.1. It is unlikely that these events are independent. In particular, it is reasonable to expect that younger adults are more likely than older adults to be college students. Note: Using the notation of conditional probability introduced later in this chapter, P ( college student | over 55 )< 0 . 08. 12.2. This would not be surprising: assuming that all the authors are independent (for example, none were written by siblings or married couples), we can view the nine names as being a random sample, so that the number N of occurrences of the ten most common names would have a binomial distribution with n = 9 and p = 0 . 096. Then P ( N = 0 ) = ( 1 0 . 096 ) 9 . = 0 . 4032. 12.3. If we assume that each site is independent of the others (and that they can be considered as a random sample from the collection of sites referenced in scientiFc journals), then P ( all seven are still good ) = 0 . 87 7 . = 0 . 3773. 12.4. Venn diagram on the right. B is the event “the degree is a bachelor’s degree,” and W is the event “the degree was earned by a woman.” The probability of the overlap is given. Subtracting this from the given probabilities for B and W gives the probabilities of the rest of those events. Those probabilities add to 0.80, so P ( neither B nor W ) = 0 . 20. (a) Because P ( W ) = 0 . 59, P ( degree was earned by a man ) = P ( not W ) = 41%. (b) P ( B and not W ) = 21%. neither B nor W 0.20 W and not B 0.30 B and not W 0.21 B and W 0.29 S 12.5. (a) Venn diagram on the right. (b) The events are { A and B } = { student is at least 25 and local } { A and not B } = { student is at least 25 and not local } { B and not A } = { student is less than 25 and local } { neither A nor B } = { student is less than 25 and not local } (c) P ( A and B ) is given. Subtracting this from the given probabilities for A and B gives P ( A and not B ) and P ( B and not A ) . Those probabilities add to 0.90, so P ( neither B nor W ) = 0 . 10. neither A nor B 0.10 A and not B 0.65 B and not A 0.20 A and B 0.05 S 12.6. Refer to the Venn diagram in the solution of Exercise 12.4. Using the notation given in that solution, P ( W | B ) = P ( B and W ) P ( B ) = 0 . 29 0 . 50 = 0 . 58. 12.7. P ( B | not A ) = P ( B and not A ) P ( not A ) = P ( B ) P ( B and A ) 1 P ( A ) = 0 . 2 0 . 3 = 2 3 . 155
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156 Chapter 12 General Rules of Probability* 12.8. Let R be the event “game is a role playing game,” while S is “game is a strategy game.” Then P ( not S ) = 1 0 . 354 = 0 . 646, and P ( R | not S ) = P ( R and not S ) P ( not S ) = P ( R ) P ( not S ) = 0 . 139 0 . 646 . = 0 . 2152 . (Note that “ R and not S ”is equivalent to R .) 12.9. Let H be the event that an adult belongs to a club, and T be the event that he/she goes at least twice a week. We have been given P ( H ) = 0 . 1 and P ( T | H ) = 0 . 4, so P ( T ) = P ( H ) P ( T | H ) = 0 . 04—about 4% of all adults go to health clubs at least twice a week. (We assume here that someone cannot attend a health club without being a member.) 12.10. Plan: Express the information we are given in terms of events and their probabilities: let A ={ the teen is online } , B the teen has a proFle } , and C the teen has commented on a friend’s blog } . Then P ( A ) = 0 . 93, P ( B | A ) = 0 . 55, and P ( C | A and B ) = 0 . 76. We want to Fnd P ( A and B and C ) .
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This note was uploaded on 11/23/2010 for the course STAT 2325151 taught by Professor T during the Spring '10 term at Waters College.

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ch12 - Chapter 12 Solutions 12.1 It is unlikely that these...

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