If P(A) = m, P(B/A̅) = 3m, P(B/A) = 6m, then what will be P(A/B)?

If $P(A) = m$, $P(B/\bar{A}) = 3m$, $P(B/A) = 6m$, then what will be $P(A/B)$?

a$\frac{2m}{1+m}$
b$\frac{4m}{1+m}$
c$\frac{7m}{1+m}$
d$\frac{9m}{1+m}$

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Answer

Official answer key

Correct option: a

Answer: (a) $\frac{2m}{1+m}$ $P(A\cap B) = m\cdot 6m = 6m^2$ and $P(\bar{A}\cap B) = (1-m)\cdot 3m = 3m - 3m^2$, so $P(B) = 3m + 3m^2$. Hence $P(A/B) = \frac{6m^2}{3m(1+m)} = \frac{2m}{1+m}$.