1. Suppose a sample space contains 6 outcomes denoted by e1, e2, . . . , e6. Let A, B
and C be the events
A = {e1, e2, e3}, B = {e3, e4, e5}, and C = {e5, e6},
and suppose probabilities are assigned as follows: P(A) = 0.4 , P(B) = 0.5 , P(C) = 0.5 , P(A n B) = 0.2 , P(B n C) = 0.2 . (a) By using a Venn diagram, or otherwise, verify that such an assignment of
probabilities is possible. (b) Find the probabilities of the events A ? B, A ? B ? C and C n B¯.
and C be the events
A = {e1, e2, e3}, B = {e3, e4, e5}, and C = {e5, e6},
and suppose probabilities are assigned as follows: P(A) = 0.4 , P(B) = 0.5 , P(C) = 0.5 , P(A n B) = 0.2 , P(B n C) = 0.2 . (a) By using a Venn diagram, or otherwise, verify that such an assignment of
probabilities is possible. (b) Find the probabilities of the events A ? B, A ? B ? C and C n B¯.
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