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
\(\frac{5}{16}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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)
= (\(\frac{1}{8} \times \frac{3}{4}\)) + (\(\frac{7}{8} \times \frac{1}{4}\))
= \(\frac{3}{32} + \frac{7}{32}\)
= \(\frac{10}{32}\)
= \(\frac{5}{16}\)
Source: Myschool Past Questions Archive (Record #36595)