Question

If P( A) = 0.8, P(B) = 0.5 and P(B | A) = 0.4, find P(A ∩ B).

Solution

Here, P(A) = 0.8, P(B) = 0.5, P(B | A) = 0.4
Now, $straight P left parenthesis straight B space left enclose straight A right parenthesis end enclose space equals space fraction numerator straight P left parenthesis straight B space intersection space straight A right parenthesis over denominator straight P left parenthesis straight A right parenthesis end fraction$
$rightwards double arrow space space space space space space 0.4 space equals space fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator 0.8 end fraction space space rightwards double arrow space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 0.32$

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Probability

If P( A) = 0.8, P(B) = 0.5 and P(B | A) = 0.4, find P(A ∩ B).

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