Question

If \( E \) and \( F \) are two independent events such that \( P(E) = \frac{2}{3} \), \( P(F) = \frac{3}{7} \), then \( P(E \,|\, F) \) is equal to:

• A. \( \frac{1}{6} \)
• B. \( \frac{1}{2} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{7}{9} \)

Hint:

For independent events, the conditional probability \( P(E \,|\, F) \) is simply \( P(E) \), as the occurrence of event \( F \) does not affect the probability of event \( E \).

Answer 1

The Correct Option is C

Since \( E \) and \( F \) are independent events, \[ P(E \,|\, F) = P(E) = \frac{2}{3}. \] Thus, the probability is \( \frac{2}{3} \).