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If events A and B are independent and \(P(A) = \frac{7}{12}\...

If events A and B are independent and \(P(A) = \frac{7}{12}\) and \(P(A \cap B) = \frac{1}{4}\), find P(B).

A.

\(\frac{3}{7}\)

B.

\(\frac{4}{7}\)

C.

\(\frac{5}{7}\)

D.

\(\frac{6}{7}\)

Correct answer is A

\(P(A) = \frac{7}{12}\)

\(P(A \cap B) = \frac{1}{4} = P(A) \times P(B)\) (Independent events)

\(\frac{1}{4} ÷ \frac{7}{12} = \frac{1}{4} \times \frac{12}{7} \)

= \(\frac{3}{7}\)