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791. If P(not A) = 0.4, P(A ∪ B) = 0.75 and A, B are given to be independent events, find the value of P(B).

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792. If P(not B) = 0.65, P( A ∪ B) = 0.85 and A, B are independent events, find the value of P(A).

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793.

For two events A and B, let P(A) = 0.4 and P(B) = p and P(A∪ B) = 0.6
(i) Find p so that A and B are independent events.
(ii) Find p so that A and B are mutually exclusive events.

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794. Given that the events A and B are such that P(A) =

1 half comma

straight P left parenthesis straight A union straight B right parenthesis space equals space 3 over 5 space and space straight P left parenthesis straight B right parenthesis space equals space straight p.

Find p if they are mutually exclusive.

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795. Given that the events A and B are such that P(A) =

1 half comma

straight P left parenthesis straight A union straight B right parenthesis space equals space 3 over 5 space and space straight P left parenthesis straight B right parenthesis space equals space straight p.

Find p if they are independent.

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796.
Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4. Find P(A ∩ B)

P(A) = 0.3, P(B) = 0.4
$straight P open parentheses straight A intersection straight B close parentheses space equals space straight P left parenthesis straight A right parenthesis cross times straight P left parenthesis straight B right parenthesis$ $open square brackets because space space straight A space and space straight B space are space independent close square brackets$
$equals space 0.3 space cross times space 0.4 space equals space 0.12$