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.
\(\frac{5}{16}\)
Correct Answer: Option D
Explanation
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)
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