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

Answer:

The probability that at least two individuals would live for an additional five years is 0.388

Step-by-step explanation:

Provided information;

For a 60-year-old's survival over five years;

P(survival of 60 years old) = 0.7

Consequently;

Probability for a 60-year-old not surviving five years;

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

Additionally, it is given;

For a 65-year-old’s survival over the next five years;

P(survival of 65 years old) = 0.4

Thus;

Probability of a 65-year-old not surviving for the next five years;

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

Moreover, it is given;

For a 70-year-old’s likelihood of survival over the next five years;

P(survival of 70 years old) = 0.2

Thus;

Probability of a 70-year-old not surviving for the next five years;

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

The probability that at least two individuals survive is;

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

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