the probability that a randomly selected 40 - year - old male will live to be 41 years old is 0.996742…

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 (round to six decimal places as needed.)

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 (round to six decimal places as needed.)

Answer

Explanation:

Step1: <Probability of independent events>

If two events (A) and (B) are independent, the probability that both (A) and (B) occur is (P(A\cap B)=P(A)\times P(B)). Let (P) be the probability that a - year - old male lives to be 41. Here (P = 0.996742). For two independent 40 - year - old males, the probability that both live to be 41 is (P_1=P\times P).

Step2: <Calculate the probability>

Substitute (P = 0.996742) into the formula (P_1). So (P_1=0.996742\times0.996742=(0.996742)^2). [ \begin{align*} (0.996742)^2&=(1 - 0.003258)^2\ &=1-2\times0.003258+0.003258^2\ &=1 - 0.006516+0.000010615\ &\approx0.993495 \end{align*} ]

Answer:

(0.993495)