If P(A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A B) - Vidyadip

Question

If P(A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find $P(A \cap B)$

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Answer

Given: P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4
We know that
By definition of conditional probability,
${P}({B} | {A})=\frac{{P}({A} \cap \mathrm{B})}{\mathrm{P}(\mathrm{A})}$
$\Rightarrow P(A \cap B)=P(B | A) P(A)$
$\Rightarrow P(A \cap B)=0.4 \times 0.8$
$\Rightarrow P(A \cap B)=0.32$

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