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5. Let A denote the event that the next item checked out at a college library is a math book, and let B be the event that the next item checked out is a history book. Suppose that P(A) 40 and P(B50. a. Why is it not the case that P(A) P(B) 1? b. Calculate P(A) c. Calculate P(A U B). d. Calculate P(4n B).

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Answer #1

Given P(A)=0.40

           P(B)=0.50

(a) why is it not the case that P(A)+P(B)=1

Ans:there are other items besides math and history books to be checked out from the library

(b) Calculate P(A')

Ans:P(A')=1-P(A)

                =1-0.40

                 =0.6

c.Calculate P(AUB)

Ans:P(AUB)=P(A)+P(B)    (since A and B are mutually exclusive)

                   =0.40+0.50

                   =0.9

d.Calculate P(A'\capB')

Ans: P(A'\capB')=(AUB)'     ( Demorgon law)

                      =1-P(AUB)

                     =1-0.9

                     =0.1

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