Question on: WAEC Mathematics - 2010
In an athletic composition, the probability that an athlete wins a 100m race is (\frac{1}{8}) and the probability that he wins in high jump is (\frac{1}{4}). What is the probability that he wins only one of the events?
A
\(\frac{3}{32}\)
B
\(\frac{7}{3}\)
C
\(\frac{5}{3}\)
D
\(\frac{5}{16}\)
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Correct Option: D
Pr. (winning 100m race) = (\frac{1}{8})
Pr. (losing 100m race) = 1 - (\frac{1}{8}) = (\frac{7}{8})
Pr. (winning high jump) = (\frac{1}{4})
Pr. (losing high jump ) = 1 - (\frac{1}{4}) = (\frac{3}{4})
Pr. (winning only one) = Pr. (Winning 100m race and losing high jump) or Pr.(Losing 100m race and winning high jump)
= ((\frac{1}{8} \times \frac{3}{4})) + ((\frac{7}{8} \times \frac{1}{4}))
= (\frac{3}{32} + \frac{7}{32})
= (\frac{10}{32})
= (\frac{5}{16})
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