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

smileycellist2

smileycellist2

Answered question

2021-09-21

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

Answer & Explanation

Tuthornt

Tuthornt

Skilled2021-09-22Added 107 answers

To determine:
Mr Solver

Mr Solver

Skilled2023-06-17Added 147 answers

Given that the probability of the man being alive in 25 years is 35, we can represent this as P(A)=35.
Similarly, the probability of the wife being alive in 25 years is 23, which can be represented as P(B)=23.
Now, we want to determine the probability that both the man and his wife will be alive in 25 years. This can be represented as the intersection of events A and B, denoted as AB.
The probability of the intersection of two independent events is given by the product of their individual probabilities. Therefore, the probability that both will be alive can be calculated as:
P(AB)=P(A)×P(B)
Substituting the given probabilities, we have:
P(AB)=35×23
Simplifying the expression, we get:
P(AB)=615=25
Therefore, the probability that both the man and his wife will be alive in 25 years is 25.
Eliza Beth13

Eliza Beth13

Skilled2023-06-17Added 130 answers

Answer:
615
Explanation:
P({man alive in 25 years})=35
P({wife alive in 25 years})=23
We want to find the probability that both the man and his wife will be alive in 25 years. We can denote this probability as P({man alive}{wife alive}).
Using the formula for the intersection of two events, we have:
P({man alive}{wife alive})=P({man alive in 25 years})×P({wife alive in 25 years})
Substituting the given probabilities, we get:
P({man alive}{wife alive})=35×23
Simplifying the expression, we find:
P({man alive}{wife alive})=615
Therefore, the probability that both the man and his wife will be alive in 25 years is 615.

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