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 0.993495
(round to six decimal places as needed.)
(b) the probability is 0.980611
(round to six decimal places as needed.)
(c) the probability is
(round to six decimal places as needed.)

Explanation:

Step1: Find the probability that all six live

The probability that a 40 - year - old male lives to 41 is \(p = 0.996742\). The probability that all six 40 - year - old males live to 41 is \(P(\text{all six live})=(0.996742)^6\)

Step2: Use the complement rule

The probability that at least one does not live is \(P(\text{at least one does not live}) = 1 - P(\text{all six live})\)
First, calculate \((0.996742)^6\approx0.980611\) (from part b, which is the probability that six live). Then \(P(\text{at least one does not live})=1 - 0.980611 = 0.019389\)

Answer:

\(0.019389\)