Given P(A) = 0.5, P(B) = 0.4, P(A⋂B) = 0.3 then P(A' / B') is equal to

Engineering

Mathematics

Conditional Probability

Question

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$P (A^{'} ∣ B^{'}) = \frac{P (A^{'} \cap B^{'})}{P (B^{'})}$
$= \frac{P (A \cup B)^{'}}{P (B^{'})}$
$= \frac{1 - P (A \cup B)}{1 - P (B)}$
$= \frac{1 - [P (A) + P (B) - P (A \cap B)]}{1 - P (B)}$
$= \frac{1 - [0.5 + 0.4 - 0.3]}{1 - 0.4}$
$= \frac{0.4}{0.6}$
$= \frac{2}{3}$

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