Single Choice

If events $$A$$ and $$B$$ are independent and $$P(A)=0.15, P(A\cup B)=0.45$$, then $$P(B)=$$

A$$\dfrac {6}{13}$$
B$$\dfrac {6}{17}$$
Correct Answer
C$$\dfrac {6}{19}$$
D$$\dfrac {6}{23}$$

Solution

Given, $$P(A) = 0.15$$, $$P(A \cup B)$$ = 0.45 We have $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ and $$P(A \cap B) = P(A).P(B)$$ Therefore, $$0.45 = 0.15 +P(B) - 0.15 P(B) $$ $$\Rightarrow 0.30 = 0.85 P(B)$$ $$\Rightarrow P(B) =$$ $$\dfrac{30}{85}$$ $$=$$ $$\dfrac{6}{17}$$

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