Jordan Graves

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

Sterling Cameron

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 $P\left(\text{man}\right)=\frac{3}{5}$ and the probability that the wife will be alive in 25 years as $P\left(\text{wife}\right)=\frac{2}{3}$.
The probability that both will be alive is given by the product of their probabilities:

Substituting the given values, we have:

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

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

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

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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