Question

The probability that a randomly selected ​-year-old male will live to be years old is . ​(a) What is the probability that two randomly selected ​-year-old male s will live to be years​ old? ​(b) What is the probability that randomly selected ​-year-old male s will live to be years​ old? ​(c) What is the probability that at least one of randomly selected ​-year-old male s will not live to be years​ old? Would it be unusual if at least one of randomly selected ​-year-old male s did not live to be years​ old?

Answer 1

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Answer:

$Probability = 0.99515$ -- (a)

$Probability = 0.98791$ -- (b)

$P(At\ least\ 1) = 0.01209$ -- (c)

Step-by-step explanation:

Given

Represent the probability that a 40-year-old male lives to 41 be P(A).

So:

$P(A) = 0.99757$

Solving (a): Two selected live to be 41

This event is represented as: AA and the probability is:

$Probability = P(A) * P(A)$

$Probability = 0.99757 * 0.99757$

$Probability = 0.99515$

Solving (b): Five selected live to be 41

This event is represented as: AAAAA and the probability is:

$Probability = P(A) * P(A)* P(A)* P(A)* P(A)$

$Probability = 0.99757 * 0.99757* 0.99757* 0.99757* 0.99757$

$Probability = 0.98791$

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:

$P(At\ least\ 1) = 1 - P(All)$

$P(At\ least\ 1) = 1 - 0.98791$

$P(At\ least\ 1) = 0.01209$

(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.