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PROBABILITY — Statistics STD 12 Commerce — Question

Gujarat BoardEnglish MediumSTD 12 CommerceStatisticsPROBABILITY2 Marks
Question
If $P(B) = 2P(A|B) = 0.4,$ then find $P(A\cap B).$
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Answer

$P(B)=2 P(A \mid B)=0.4$
$ \therefore P(B)=0.4,2 P(A \mid B)=0.4$
$ \therefore P(A \mid B)=\frac{0.4}{2}=0.2$
$ \text { Now, } P(A \mid B)=\frac{P(A \cap B)}{P(B)}$
$ \therefore P(A \cap B)=P(A \mid B) \cdot P(B)$
$ =0.2 \times 0.4=0.08$

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