We have an answer to "The probability that a man will be alive..."

Jordan Graves

Answered question

2023-03-30

The probability that a man will be alive in 25 years is 3/5, and the probability that his wifewill be alive in 25 years is 2/3
Determine the probability that both will be alive

Answer & Explanation

Sterling Cameron

Beginner2023-03-31Added 6 answers

To determine the probability that both the man and his wife will be alive in 25 years, we can multiply their individual probabilities of being alive.
Let's denote the probability that the man will be alive in 25 years as

P (man) = \frac{3}{5}

and the probability that the wife will be alive in 25 years as

P (wife) = \frac{2}{3}

.
The probability that both will be alive is given by the product of their probabilities:

P (both alive) = P (man) \times P (wife)

Substituting the given values, we have:

P (both alive) = \frac{3}{5} \times \frac{2}{3}

To simplify the expression, we can cancel out the common factors:

P (both alive) = \frac{3 \times 2}{5 \times 3}

The numerator simplifies to 6, and the denominator simplifies to 15:

P (both alive) = \frac{6}{15}

To express the probability in its simplest form, we can further reduce the fraction:

P (both alive) = \frac{2}{5}

Therefore, the probability that both the man and his wife will be alive in 25 years is

\frac{2}{5}

, which is equivalent to 0.4.

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