The probabilities of events A and B are given by P(A) = 0.6 and P(B) = 0.22 respectively.?

The probabilities of events A and B are given by P(A) = 0.6 and P(B) = 0.22 respectively.


Find


(a) P(A ⋃ B) , if A and B are mutually exclusive events.


(b) P(A ⋃ B) , if A and B are independent events.


(c) P(A ⋂ B ' ) , if A and B are independent events.

The probabilities of events A and B are given by P(A) = 0.6 and P(B) = 0.22 respectively.?
1) P(A ⋃ B) = P(A) + P(B) - P(A ⋂ B)


If A and B are mutually exclusive events then P(A ⋂ B) = 0 and


P(A ⋃ B) = P(A) + P(B) = 0.6 + 0.22 = 0.82





2) P(A ⋃ B) = P(A) + P(B) - P(A ⋂ B)


If A and B are independent events then P(A ⋂ B) = P(A) P(B)


and P(A ⋃ B) = 0.6 + 0.22 - (0.6 * 0.22) = 0.688





3) If A and B are independent events then A and B' are independent events, and


P(A ⋂ B ' ) = P(A) P(B') = P(A) (1 - P(B)) = 0.6 * (1 - 0.22) = 0.468





Dan

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