Question

1) Sunshine Insurance offers life insurance to men age 70. Mortality tables indicate the likelihood of a 70-year-old man surviving another year is .92. If the policy is offered to six men age 70 a. What is the probability all six men survive the year? b. What is the probability that at least one survives?

Answer 1

60.6%

0.0003%

Explanation:

Because they are independent events, the final probability will be the multiplication of each event, that is, 0.92 multiplied 6 times, in other words:

0.92 ^ 6 = 0.606

that is to say that the probability that the 6 men survive is 60.6%

Now, to calculate that at least one survives, it means that 5 died, the probability that one dies is 1 - 0.92 = 0.08, and how they are 5 would be:

0.08 ^ 5 = 0.0000032768

Then multiplied by 0.92, which is that one survives, we are left with:

0.0000032768 * 0.92 = 0.00000301465

Which means that the probability of one surviving is 0.0003%, it is a very low probability because the probability of surviving is really high.