Question 29

P and Q are independent events. The odds in favour of P and Q are 3:2 and 5:4, respectively. Find the probability that only one of the two events occurs.

Name: P and Q are independent events. The odds in favour of P and Q are 3:2 and 5:4, respectively. Find the probability that only one of the two events occurs.
Uploaded: 2026-06-14T12:16:07.877336+05:30
Duration: 4 min 54 s
Description: P and Q are independent events. The odds in favour of P and Q are 3:2 and 5:4, respectively. Find the probability that only one of the two events occurs.

Solution

Probability of A happening = $$\frac{3}{3+2}=\frac{3}{5}$$ and,
Probability of B happening = $$\frac{5}{5+4}=\frac{5}{9}$$.
Probability that only one of the two events occurs = A occurs and B does not + B occurs and A does not
==> $$\frac{3}{5}\left(1-\frac{5}{9}\right)+\left(1-\frac{3}{5}\right)\frac{5}{9}=\frac{22}{45}$$.

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