Question

the probability that a randomly selected 40 - year - old male will live to be 41 years old is 0.996742, according to the national vital statistics report, vol. 71, no. 1
(a) what is the probability that two randomly selected 40 - year - old males will live to be 41 years old?
(b) what is the probability that six randomly selected 40 - year - old males will live to be 41 years old?
(c) what is the probability that at least one of six randomly selected 40 - year - old males will not live to be 41 years old? would it be unusual if at least one of six randomly selected 40 - year - old males did not live to be 41 years old?
(a) the probability is
(round to six decimal places as needed.)

Explanation:

Step1: Use the multiplication rule for independent events

If two events \(A\) and \(B\) are independent, \(P(A\cap B)=P(A)\times P(B)\). Let \(P\) be the probability that a 40 - year - old male lives to 41. Here \(P = 0.996742\). For two independent 40 - year - old males, the probability that both live to 41 is \(P\times P\).

$$0.996742\times0.996742$$

Step2: Calculate the product

$$0.996742\times0.996742=(1 - 0.003258)\times(1 - 0.003258)=1-2\times0.003258 + 0.003258^{2}$$

$$=1-0.006516+0.000010615564\approx0.993495$$

Answer:

\(0.993495\)