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JAMB Mathematics 2012 Paper

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Question : 39

Total: 48

The probabilities that a man and his wife live for 80 years are

\frac{2}{3}

\frac{3}{5}

respectively. Find the probability that at least one of them will live up to 80 years

$\frac{2}{15}$
$\frac{3}{15}$
$\frac{7}{15}$
$\frac{13}{15}$

Solution:

Concept:

Use the complement rule:

P(\text{at least one lives}) = 1 - P(\text{both die})

.

Explanation:

Probability that the man does not live to 80 is

1 - \frac{2}{3} = \frac{1}{3}

.

Probability that the wife does not live to 80 is

1 - \frac{3}{5} = \frac{2}{5}

.

Probability that neither lives to 80 is

\frac{1}{3} \times \frac{2}{5} = \frac{2}{15}

.

Thus, probability that at least one lives to 80 is

1 - \frac{2}{15} = \frac{13}{15}

.

Answer:

\frac{13}{15}

Correct option: D.

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