Question

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

• A. $0$
• B. $\frac{15}{24}$
• C. $\frac{13}{24}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{13}{24}$

$P\left(A\right)=\frac{3}{8}$

$P\left(B\right)=\frac{1}{6}$
$P(A\cap B)=0$
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)$
$P(A\cup B)=\frac{3}{8}+\frac{1}{6}-0$

$P(A\cup B)=\frac{18+8}{48}$

$P(A\cup B)=\frac{13}{24}$