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Answer:
[tex]Probability = 0.99515[/tex] -- (a)
[tex]Probability = 0.98791[/tex] -- (b)
[tex]P(At\ least\ 1) = 0.01209[/tex] -- (c)
Step-by-step explanation:
Given
Represent the probability that a 40-year-old male lives to 41 be P(A).
So:
[tex]P(A) = 0.99757[/tex]
Solving (a): Two selected live to be 41
This event is represented as: AA and the probability is:
[tex]Probability = P(A) * P(A)[/tex]
[tex]Probability = 0.99757 * 0.99757[/tex]
[tex]Probability = 0.99515[/tex]
Solving (b): Five selected live to be 41
This event is represented as: AAAAA and the probability is:
[tex]Probability = P(A) * P(A)* P(A)* P(A)* P(A)[/tex]
[tex]Probability = 0.99757 * 0.99757* 0.99757* 0.99757* 0.99757[/tex]
[tex]Probability = 0.98791[/tex]
Solving (c): At least one of five selected will not live to be 41.
In (b), we calculate the probability that all 5 lives to be 41.
When this is subtracted from 1, it gives the probability that at least one of them will not is:.
So, we have:
[tex]P(At\ least\ 1) = 1 - P(All)[/tex]
[tex]P(At\ least\ 1) = 1 - 0.98791[/tex]
[tex]P(At\ least\ 1) = 0.01209[/tex]
(c ii).
It will be unusual because the probability that at least one of the selected 5 will not live to 41 is very low.
