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Question

Let A,B are mutually independent events then show that ¯¯¯¯A,B are also mutually independent events.

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Solution

Given the sets A & B are
mutually independent.
Then P(AB)=P(A).P(B).
Now, we are to prove ¯A & B
are also mutually indendents
Now,
P(¯AB)
=P(B)P(AB)[¯AB=BAB]
=P(B)P(A).P(B)
=P(B)[1P(A)]
=P(B)P(¯A)[1P(A)=P(¯A)]
=P(¯A).P(B)
so, ¯A,B are mutually independent
sets.


1163298_1191537_ans_8474ce5dd9014cd8ace62dcaab09aa27.jpg

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