Question

There are three persons aged 60, 65 and 70 years old. The survival probabilities for these

three persons for another 5 years are 0.7.0.4 and 0.2 respectively. What is the probability
that at least two of them would survive another five years?
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Answer 1

Probability that at least two of them would survive another five years = 0.388

Explanation:

We are given;

Probability of Survival of 60 years old for the next 5 years;

P(60 years old surviving) = 0.7

Thus;

Probability of 60 years old not surviving for the next 5 years;

P(60 years old not surviving) = 1 - 0.7 = 0.3

Also,given;

Probability of Survival of 65 years old for the next 5 years;

P(65 years old surviving) = 0.4

Thus;

Probability of 65 years old not surviving for the next 5 years;

P(65 years not surviving) = 1 - 0.4 = 0.6

Also,given;

Probability of Survival of 70 years old for the next 5 years;

P(70 years old surviving) = 0.2

Thus;

Probability of 70 years old not surviving for the next 5 years;

P(70 years not surviving) = 1 - 0.2 = 0.8

Probability that at least two survived is;

P(at least 2 surviving) = [P(60 surviving) x P(65 surviving) x P(70 not surviving)] + [P(60 surviving) x P(65 not surviving) x P(70 surviving)] + [P(60 not surviving) x P(65 surviving) x P(70 surviving)] + [P(60 surviving) x P(65 surviving) x P(70 surviving)]

P(at least 2 surviving) = [(0.7)(0.4)(0.8)] + [(0.7)(0.6)(0.2)] + (0.3)(0.4)(0.2) + [(0.7)(0.4)(0.2)]

P(at least 2 surviving) = 0.224 + 0.084 + 0.024 + 0.056

P(at least 2 surviving) = 0.388