Question

If A and B are two events such that P(A) = \(\rm \frac{1}{2}\), P(B) = \(\rm \frac{1}{3}\), P(A/B) = \(\rm \frac{1}{4}\), then P(A U B) is
1. \(\rm \frac{1}{3}\)
2. \(\rm \frac{3}{4}\)
3. \(\rm \frac{1}{4}\)
4. \(\rm \frac{1}{2}\)
5. \(\rm \frac{4}{5}\)

Answer 1

Correct Answer - Option 2 : \(\rm \frac{3}{4}\)

Concept:

P (A/B) = \(\rm \frac{P(A \cap B)}{P(B)}\)

P (A U B) = P (A) + P (B) - \(\rm P(A \cap B)\)

Calculation:

P (A) = \(\rm \frac{1}{2}\), P (B) = \(\rm \frac{1}{3}\), P (A/B) = \(\rm \frac{1}{4}\)

P (A/B) = \(\rm \frac{P(A \cap B)}{P(B)}\)

\(\rm \frac{1}{4}\) = \(\rm \frac{P(A \cap B)}{\rm \frac{1}{3}}\)

\(\rm P(A \cap B)\) = \(\rm \frac{1}{12}\)

P (A U B) = P (A) + P (B) - \(\rm P(A \cap B)\)

= \(\rm \frac{1}{2}\) + \(\rm \frac{1}{3}\)- \(\rm \frac{1}{12}\)

= \(\rm \frac{6 + 4 - 1}{12}\)

= \(\rm \frac{9}{12}\)

= \(\rm \frac{3}{4}\)