If events A and B are independent and P(A) = 0.15, P(A∪B) = 0.45, then P(B) =

Engineering

Mathematics

Conditional Probability

Question

$\frac{6}{13}$

$\frac{6}{17}$

$\frac{6}{19}$

$\frac{6}{23}$

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Given, P(A) = 0.15, P(A∪B) = 0.45
We have P(A∪B) = P(A) + P(B) − P(A∩B)
and P(A∩B) = P(A).P(B
Therefore, 0.45 = 0.15 + P(B) − 0.15P(B)
⇒ 0.30 = 0.85P(B)

$\Rightarrow P (B) = \frac{30}{85} = \frac{6}{17}$

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