Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find P(neither A nor B)

Solution

Here P(A) = 0.3, P(B) = 0.6
$therefore space space space space space space space space space space straight P space open parentheses straight A with bar on top close parentheses equals space 1 minus straight P left parenthesis straight A right parenthesis space equals space 1 minus 0.3 space equals 0.7 space space space space space space space space space space space space space straight P open parentheses straight B with bar on top close parentheses space equals space 1 minus space straight P left parenthesis straight B right parenthesis space equals space 1 minus 0.6 space equals space 0.4$
P (neither A nor B) = $straight P left parenthesis straight A to the power of straight c space and space straight B to the power of straight c right parenthesis space equals space straight P left parenthesis straight A to the power of straight c space intersection straight B to the power of straight c right parenthesis$
$equals space straight P space open parentheses left parenthesis straight A space union space straight B right parenthesis to the power of straight c close parentheses space equals space 1 minus space straight P left parenthesis straight A space union space straight B right parenthesis space space equals space 1 minus 0.72 space equals 0.28$

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Probability

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find P(neither A nor B)

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