Five people buy individual insurance policies. According to the research, the probability of each of these people not filing a claim for at least 5 years is. The probability that all 5 have not filed a claim after 5 years is, and the probability that exactly 3 will have filed a claim after 5 years is. Reset Next

The complete question is;

Five people buy individual insurance policies. According to the research, the probability of each of these people not filing a claim for at least 5 years is 2/3.

The probability that all 5 have not filed a claim after 5 years is A: 0.132 B: 0.868 C: 1, and the probability that exactly 3 will have filed a claim after 5 years is A: 0.016 B: 0.033 C: 0.067

Answer:

1) P (all 5 file no claim after 5 years) = 0.132

2) P (exactly 3 file claim after 5 years) = 0.033

Step-by-step explanation:

1) we are told that the probability of each of these people not filing a claim for at least 5 years is 2/3.

Thus, for all 5 of them,

The probability will be;

P (all 5 file no claim after 5 years) = (2/3) ^5 = 0.1317 ≈ 0.132

2) since probability of each not filing a claim for last 5 years = 2/3

Then probability of each filing a claim after 5 years = 1 - 2/3 = 1/3

So, P (exactly 3 file claim after 5 years) = (1/3) ^3 ≈ 0.037.

The closest answer is 0.033.