The probabilities of winning a race by three persons A, B, and C are 1/2, 1/4 and 1/4 respectively.They run two races.The probability of A winning the second race when B wins the first race is

Engineering

Mathematics

Conditional Probability

Question

$\frac{1}{3}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{2}{3}$

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A winning the second race when B winning the first race ⇒ A and B are independent events
Therefore the required probability is A winning the race which is $\frac{1}{2}$
Hence, The correct answer is $\frac{1}{2}$ .

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