Given $P(A) = 0.5,\ P(B) = 0.4,\ P(A \cap B) = 0.3,$then $P\left( \frac{A'}{B'} \right)$is equal to

Question

Dr. Abubacker · Accepted Answer

(c)
$P\left( A^{'} \middle| B^{'} \right) = \frac{P(A^{'} \cap B^{'})}{P(B^{'})}$
$= \frac{P(A \cup B^{'})}{P(B^{'})}$
$= \frac{1 - P(A \cup B)}{1 - P(B)}$
$= \frac{1 - P(A) + P(B) - P(A \cap B)}{1 - P(B)}$
$= \frac{1 - \lbrack - 0.5 + 0.4 - 0.3\rbrack}{1 - 0.4} = \frac{0.4}{0.6} = \frac{2}{3}$

Q. Given $P(A) = 0.5,\ P(B) = 0.4,\ P(A \cap B) = 0.3,$then $P\left( \frac{A'}{B'} \right)$is equal to

Explanation

Reviewed by Dr. Abubacker

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