Question

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

Answer 1

Answer:

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

Step-by-step 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