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

Chapter 3, Problem 24E

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QUESTION:

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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QUESTION:

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 ?

ANSWER:

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

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