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?
- \(\frac{3}{32}\)
- \(\frac{7}{3}\)
- \(\frac{5}{3}\)
-
\(\frac{5}{16}\)
The correct answer is: 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)
= (\(\frac{1}{8} \times \frac{3}{4}\)) + (\(\frac{7}{8} \times \frac{1}{4}\))
= \(\frac{3}{32} + \frac{7}{32}\)
= \(\frac{10}{32}\)
= \(\frac{5}{16}\)