An insurance company sells policies to 5 men all of identical age and in good health the probability that's the man of This particular age will be alive 30 year's in 2/3 find the probability in that 30 year's?

Question

Answer

Probability of a Man being alive in 30 years

Given that an insurance company sells policies to 5 men of identical age and good health, with a probability of 2/3 that a man of this particular age will be alive in 30 years, we need to find the probability of a man being alive in that time period.

Understanding the Problem

Let's assume that the probability of a man being alive at any given year is p. Therefore, the probability of a man being alive in 30 years is also p. Given that p is 2/3, we can substitute this value into our equation.

Calculating the Probability

Using the formula for probability, we have:

p = 2/3

Since the men are identical in age and health, the probability of each man being alive in 30 years is the same. Therefore, we can calculate the probability of a man being alive in 30 years using the following equation:

Probability of a man being alive in 30 years = p^5

Substituting the value of p into the equation:

Probability of a man being alive in 30 years = (2/3)^5

Using the exponent rule, we can simplify the equation:

Probability of a man being alive in 30 years = 32/243

Interpretation

Therefore, the probability that all 5 men will be alive in 30 years is 32/243. This means that out of every 243 scenarios, we can expect that all 5 men will be alive in 30 years in approximately 32 of those scenarios.

It is important to note that this calculation assumes that the probability of each man being alive in any given year is independent of the others. It is also based on the given information that all 5 men are of identical age and in good health.

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