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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
If P(A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A|B)
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Answer

Given: P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4
By definition of conditional probability $P(B | A)=\frac{P(A \cap B)}{P(A)}$
$\Rightarrow P(A \cap B) = P(B | A) ~P(A) = 0.32$
$Now,~ P(A | B)=\frac{0.32}{0.5}=0.64$
$\Rightarrow$ P(A|B) = 0.64

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