two insurance policies, each with a death benefit of 10,000 and a one-time premium of 500, are sold to a married couple, one for each person. the policies will expire at the end of the tenth year. the probability that only the wife will survive at least ten years is 0.025, the probability that only the husband will survive at least ten years is 0.01, and the probability that both of them will survive at least ten years is 0.96. calculate the expected excess of premiums over claims, given that the husband survives at least ten years.

The number of possible outcomes is divided by the total number of possible outcomes to determine probability. Odds are not the same as probability. Odds are calculated by dividing the chance of a given event by the probability that it won't.

Let x denote the excess of premiums over claims

a)Only the husband survives this occurs with probability 0.01

In this case the claims are 10000 while the premiums collected are

2*500 = 1000

∴ x = 1000 - 10000

= -9000

b) Both husband and wife survive this occurs with probability 0.96

In case the claims are 0, so with the premiums being before 1000 we have

∴x = 1000 - 0

= 1000

The probability that the husband survives is the sum of above probabilities = 0.01 + 0.96 = 0.97

E(X/husband survives)= [tex]\frac{(-9000)(0.01) + (1000)(0.96)}{0.97}[/tex]

= 896.9 ≈ 897

To learn more about calculating probability from the given link

https://brainly.com/question/24756209

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