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Probability

A and B are m...

Question

$A a n d B a r e m u t u a l l y e x c l u s i v e e v e n t s o f a n e x p e r i m e n t .$
$I f P (¯ A) = 0.65, P (A \cup B) = 0.65 a n d P (B) = P .$
$F i n d t h e v a l u e o f P .$

A

0.70

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B

0.30

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C

0.63

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D

0.35

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Solution

The correct option is B 0.30
$W e k n o w P (A) = 1 - P (¯ A)$

$= 1 - 0.65 = 0.35 a n d$

$P (A \cup B) = P (A) + P (B) - P (A \cap B)$

$\Rightarrow 0.65 = 0.35 + P (B) - 0$

$∵ A a n d B a r e m u t u a l l y e x c l u s i v e e v e n t s$

$\Rightarrow P (B) = 0.65 - 0.35 = 0.30$

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