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Probability

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Question : 90 of 127

Marks: +1, -0

For a 60 year old person living upto the age of 70 , it is

7:5

against him and for another 70 years old person surviving upto the age of 80 , it is

5:2

against him. The probability that only one of them will survive for 10 years more is :

$\frac{15}{42}$
$\frac{39}{84}$
$\frac{49}{84}$
$\frac{40}{84}$

Solution:

Concept:

Convert odds against to probabilities, then find probability that exactly one survives.

Explanation:

For the 60-year-old: odds against survival are

7:5

, so

P(\text{survives}) = \frac{5}{7+5} = \frac{5}{12}

, and

P(\text{does not survive}) = \frac{7}{12}

.

For the 70-year-old: odds against survival are

5:2

, so

P(\text{survives}) = \frac{2}{5+2} = \frac{2}{7}

, and

P(\text{does not survive}) = \frac{5}{7}

.

The probability that only one survives is:

P(\text{60 survives and 70 does not}) + P(\text{60 does not and 70 survives})

= \frac{5}{12} \times \frac{5}{7} + \frac{7}{12} \times \frac{2}{7}

= \frac{25}{84} + \frac{14}{84} = \frac{39}{84}

.

Answer:

\frac{39}{84}

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