Test Index

Probability

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Question : 95 of 127

Marks: +1, -0

The probabilities of Mr.

X

Y

not living for one more year are

\frac{1}{9}

\frac{1}{7}

respectively. The probability of living one more year of either one or both is

$\frac{2}{21}$
$\frac{6}{63}$
$\frac{15}{63}$
$\frac{62}{63}$

Solution:

Concept:

The probability that at least one lives is 1 minus the probability that both die.

Explanation:

Given:

P(\text{X not living}) = \frac{1}{9}

and

P(\text{Y not living}) = \frac{1}{7}

.

So,

P(\text{X living}) = 1 - \frac{1}{9} = \frac{8}{9}

and

P(\text{Y living}) = 1 - \frac{1}{7} = \frac{6}{7}

.

We need

P(\text{either one or both live}) = 1 - P(\text{both not live})

.

P(\text{both not live}) = \frac{1}{9} \times \frac{1}{7} = \frac{1}{63}

.

Thus, required probability =

1 - \frac{1}{63} = \frac{62}{63}

.

Answer:

\frac{62}{63}

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