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If A and B are two events such that $P (A / B) = 0.6, P (B / A) = 0.3, P (A) = 0.1$ then $P (\bar{A} \cap \bar{B}) =$

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0.88

0.12

0.6

0.4

answer is A.

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Detailed Solution

$P (\frac{A}{B}) = 0.6$

$P (\frac{B}{A}) = 0.3$

$P (A) = 0.1$

$P (\frac{B}{A}) = \frac{P (A \cap B)}{P (A)}$

$P (A \cap B) = 0.03$

$P (\frac{A}{B}) = \frac{P (A \cap B)}{P (B)}$

$P (B) = \frac{0.03}{0.6} = 0.05$

$P (\bar{A} \cap \bar{B}) = P (\bar{A \cup B}) = 1 - P (A \cup B) = 0.88$

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