Question

1) Sunshine Insurance offers life insurance to men age 80. Mortality tables indicate the likelihood of a 80-year-old man surviving another year is.94. If the policy is offered to six men age 80 a. What is the probability all eight men survive the year? b. What is the probability that at least one survives?

Answer 1

Let X be a random variable that denotes the number of men age 80 who survives another year and it follows a binomial distribution with parameter n=6 and p=0.94. Hence, XBinom(n=6, p=0.94). The probability mass function of a binomial distribution is given below: p' (1-P) a. The probability of all eight men survive the year is calculated as follows: P(X=6) = (0)(0.94) (1–0,94)** 6! -x0.94 x 0.06° 6!6-6)! =0.94 = 0.6898 Hence, the probability of all eight men survives the year is 0.6898 b.

The probability that at least one survives is calculated as follows: P(X21)=1-P(X <1) =1-P(X=0) =1- 1-60)(0.94) (1 -0.94)60 6! =1- -x1x0.06 0!(6-0) = 1-0.06% =1-(4.6656x10-6) = 0.9999 Hence, the probability that at least one survives is 0.9999