Question

If \(E\) and \(F\) are two independent events such that \[ P(E)=\frac{3}{10}, \qquad P(E\cup F)=\frac{1}{2}, \] then \[ P(E\mid F)-P(F\mid E) \] is equal to \[ \_\_\_\_. \]

• A. \( \frac{2}{7} \)
• B. \( \frac{3}{35} \)
• C. \( \frac{1}{70} \)
• D. \( \frac{1}{7} \)

Hint:

For independent events, conditional probabilities collapse immediately: \( P(A|B) = P(A) \). This avoids wasting time setting up complex fractions for the final subtraction step.

Answer 1

The Correct Option is C