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# Show that if one event A is contained in another event B

ISBN: 9780321629111 32

## Solution for problem 24E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 24E

Show that if one event ?A ?is contained in another event ?B ?(i.e., ?A ?is a subset of ?B?), thenP(A) ? P(B) . [?Hint: ?For such ?A ?and ?B, A ?and B?A ’, are disjoint and B = A ?(B?A ’),as can be seen from a Venn diagram.] For general ?A ?and ?B, ?what does this imply about the relationship among P(A?B), P(A?B)and ?

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Solution : Step1 : It is given that one event A is contained in another event B (i.e., A is a subset of B) that means A and BA are disjint and B=A(BA ’). We have to prove P(A) P(B) . and also want to find what does is imply about the relationship among P(AB), P(A) and P(AB). tep 2: a) We have to prove P(A) P(B) By considering the venn diagram Since B and BA are dijoint and also B=A (BA ). That means p(B)= p(A (BA )) =p(A) +p(BA ) By using the fact p(B A 0 It is clear that p(B) p(A).

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