# Given, P(A) = 0.5, P(B) = 0.4, P(A∩B) = 0.3,

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

(a) $\frac{1}{3}$

(b) $\frac{1}{2}$

(c) $\frac{2}{3}$

(d) $\frac{3}{4}$

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Answer: (C)  $\frac{2}{3}$

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

$\frac{1-P(A\,\cup\,B)}{1-P(B)} = \frac {1-[P(A)+P(B)-P(A\,\cap\,B)]}{1-P(B)}$

$= \frac{1-[0.5+0.4-0.3]}{1-0.4}=\frac{0.4}{0.6}=\frac{2}{3}$