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If P(A) = 3K, P(B) = K, where ‘A’ and ‘B’ are two independent events and P(both A and B occur) = 1/3, then
P(exactly one of A, B occurs) is:

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$\frac{2}{3}$

$\frac{1}{9}$

$\frac{1}{3}$

$\frac{2}{9}$

answer is B.

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Detailed Solution

$P (A \cap B) = P (A) \cdot P (B) \Rightarrow 3 K^{2} = \frac{1}{3} \Rightarrow K = \frac{1}{3}$

P(exactly one of A, B occurs) $= P (A) + P (B) - 2 P (A \cap B) = 3 k + k - \frac{2}{3} = \frac{4}{3} - \frac{2}{3} = \frac{2}{3}$

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