Question: Let A, B, C, D, and E be five events such that P(A) = P(B) = = P(E) = k and P(A B)

Let A, B, C, D, and E be five events such that P(A) = P(B) = ··· = P(E) = k and P(A ∩ B) = P(A ∩ C) = ··· = P(D ∩ E) = p. Moreover, at least one of the events A, . . . , E must occur, and the intersection of any three events among A, B, . . . , E is empty. (i) Find p if k = 0.3. (ii) Omit the assumption that at least one of the events must occur and determine all possible values of k if it is known that p = 0.01.

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