Question

The probability that A can win a race is 3/8 and probability that B can win it is 1/6.If both ran in a race, find the probability that one of them will win the race, assume that both cannot win together.

Answer 1

Given:
Probability that A will win the race, P(A) = $\frac{3}{8}$
And,
Probability that B will win the race, P(B) = $\frac{1}{6}$
Events A and B are mutually exclusive.
∴ $\mathrm{P}(\mathrm{A}\cap \mathrm{B})=0$
And,
P(A $\cup$ B) = P(A) + P(B) $-$ P(A $\cap$ B)

= $\frac{3}{8}+\frac{1}{6}-0=\frac{13}{24}$

∴ Probability that one of them will win the race = $\frac{13}{24}$