Sue and Ann are taking the same English class and decide to study together. The

Question

Sue and Ann are taking the same English class and decide to study together. The probability that Sue makes an A in English is 0.42 and the probability that Ann makes an A is 0.39. The probability they both make A's is 0.22. a) Are the events "Ann passes" and "Sue passes" independent events? Are the events "Ann passes" and "Sue passes mutually exclusive events? (b) What is the probability that Sue makes an A but Ann doesn't? (c) What is the probability neither girl makes an A? (d) If Sue makes an A, what then is the conditional probability that Ann will also make an A? (e) If Ann makes an A, what then is the conditional probability that Sue will not make an A? sue and ann are taking the same English but they not study together, so whether one passes will be independent of whether the other passes. In other words "Sue passes and "Ann passes" are assumed to be independent events. The probability that Sue passes English is 0.9 and the probability that Ann passes English is 0.6. (a) What is the probability both girls pass English? (b) What is the probability neither girl passes English? (c) If Ann passes, what then is the conditional probability that Sue also passes? (c) Are the events Ann passes" and "Sue passes" mutually exclusive events? Tom and Alice work independently problem (i.e whether one of them solves it does not affect the chances that the other will solve it). The probability that Tom solves the problem is 0.25 and the probability that Alice in an attempt to solve a certain whether solves the problem is 0.6 (a) What is the probability that the problem will be solved by at least one person? (b) If you find out later that the problem has been solved by at least one person, what is the conditional probability that Tom solved it?

Explanation / Answer

1)

probabilty at least one makes A =0.42+0.39-0.22 =0.59

b) probabilty sue makes an A and Ann does not =0.42-0.22=0.20

c) probability neither makes =1-0.59=0.41

2)b) neither girl passess =0.1*0.4=0.04

3)a) probabilty =1-0.25*0.6=0.85

b)probabilty =0.25/0.85 =0.2941

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