waecmaths question:
In an athletics competition, the probability that an athlete wins a 100 m race is $\tfrac{1}{8}$ and the probability that he wins in high jump is $\tfrac{1}{4}$. What is the probability that he wins only one of the events
Option A:
$\tfrac{3}{32}$
Option B:
$\tfrac{3}{16}$
Option C:
$\tfrac{7}{32}$
Option D:
$\tfrac{5}{16}$
waecmaths solution:
$\begin{align} & \Pr (R)=\frac{1}{8} \\ & \Pr (R')=1-\tfrac{1}{8}=\tfrac{7}{8} \\ & \Pr (H)=\frac{1}{4} \\ & \Pr (H')=1-\tfrac{1}{4}=\tfrac{3}{4} \\ & \Pr (R\cap H')=(\tfrac{1}{8}\times \tfrac{3}{4})=\tfrac{3}{32} \\ & \Pr (R'\cap H)=\tfrac{7}{8}\times \tfrac{1}{4}=\tfrac{7}{32} \\ & \Pr (R\cap H')+Pr(R'\cap H)=\tfrac{3}{32}+\tfrac{7}{32}=\tfrac{10}{32}=\tfrac{5}{16} \\\end{align}$
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