Question

If two events A and B. If odds against A are 2:1 and those in favour of \( A \cup B \) are 3:1, then

• A. \( \frac{1}{2} \leq P(B) \leq \frac{3}{4} \)
• B. \( \frac{5}{12} \leq P(B) \leq \frac{3}{4} \)
• C. \( \frac{1}{5} \leq P(B) \leq \frac{3}{4} \)
• D. None of these

Hint:

To find the probability of events in combination, use the relationship \( P(A \cup B) = P(A) + P(B) - P(A \cap B) \).

Answer 1

The Correct Option is B

Step 1: Using probability relations.
The odds against \( A \) give \( P(A) = \frac{1}{3} \), and the odds in favor of \( A \cup B \) give \( P(A \cup B) = \frac{3}{4} \). By using these values, we can solve for the range of \( P(B) \).

Step 2: Conclusion.
The probability \( P(B) \) lies between \( \frac{5}{12} \) and \( \frac{3}{4} \), corresponding to option (2).