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A and B are two independent events such that \(P(A) = \frac{...

A and B are two independent events such that \(P(A) = \frac{2}{5}\) and \(P(A \cap B) = \frac{1}{15}\). Find \(P(B)\)

A.

\(\frac{3}{5}\)

B.

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

C.

\(\frac{1}{6}\)

D.

\(\frac{2}{15}\)

Correct answer is C

For independent events A and B, \(P(A \cap B) = P(A) \times P(B)\)

\(\frac{1}{15} = \frac{2}{5} \times P(B)\)

\(P(B) = \frac{1}{15} \div \frac{2}{5}\)

\(P(B) = \frac{1}{6}\)