Question

Let A and B independent events, $P(A)=0.3$ and $P(B)=0.4$.Find:
(A)$P(A\cap B)$
(B)$P(A\cup B)$
(C)$P(A|B)$
(D)$P(B|A)$

Answer 1

$P(A)=0.3$
$P(B)=0.4$
$A$ and $B$ are independent events.

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$(i)P(A∩B)$
$=P(A).P(B)$
$=0.3\times0.4$
$=0.12$

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$(ii)P(A∪B)$
$=P(A)+P(B)-P(A).P(B)$
$=0.03+0.4-0.3\times 0.4$
$=0.7-0.12$
$=0.58$

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(iii)P(A|B)$$=\frac{P(A∩B)}{P(B)}
=\frac{P(A).P(B)}{P(B)}$$=\frac{0.12}{0.4}
$=0.3$

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(iv)P(B|A)$$=\frac{P(A∩B)}{P(A)}
$=\frac{P(A).P(B)}{P(A)}$
$=\frac{0.12}{0.3}$
$=0.4$