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WAEC Mathematics 2010 Paper

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Question : 34

Total: 49

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?

$\frac{3}{32}$
$\frac{7}{3}$
$\frac{5}{3}$
$\frac{5}{16}$

Solution:

Concept:

Find the probability of winning exactly one of two independent events.

Explanation:

Let

W_1

be winning the 100 m race and

W_2

be winning the high jump.

Given:

P(W_1) = \frac{1}{8}

, so

P(\text{lose } 100\text{ m}) = 1 - \frac{1}{8} = \frac{7}{8}

.

Given:

P(W_2) = \frac{1}{4}

, so

P(\text{lose high jump}) = 1 - \frac{1}{4} = \frac{3}{4}

.

Winning only one event means: win the 100 m and lose the high jump, OR lose the 100 m and win the high jump.

So, probability

= \left(\frac{1}{8} \times \frac{3}{4}\right) + \left(\frac{7}{8} \times \frac{1}{4}\right)

.

= \frac{3}{32} + \frac{7}{32} = \frac{10}{32} = \frac{5}{16}

.

Answer:

\frac{5}{16}

, which is option D.

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