The probability of man living for 50 years

Praveen 188-402

Praveen 188-402

Answered question

2022-07-31

The probability of man living for 50 years from today is 0.6 and probability of his wife living for 50 years from today is 0.5. Find the probability that both are alive after 50 years and one of them is dead?

Answer & Explanation

xleb123

xleb123

Skilled2023-06-02Added 181 answers

To find the probability that both the man and his wife are alive after 50 years and one of them is dead, we can use the concept of joint probability.
Let's denote the event the man is alive after 50 years as A and the event the wife is alive after 50 years as B.
The probability of the man living for 50 years is given as P(A)=0.6, and the probability of the wife living for 50 years is given as P(B)=0.5.
To find the probability that both are alive after 50 years and one of them is dead, we can calculate the probability of the intersection of events A and B when exactly one of them is dead.
The probability of one of them being dead is the complement of both being alive, which can be calculated as 1P(AB).
Using the properties of probability, we have:
P(AB)=P(A)P(AB)
P(AB)=0.6P(AB)
Given that P(A)=0.6 and P(B)=0.5, we can substitute these values into the equation:
0.6P(AB)=0.6P(A)·P(B)
0.6P(AB)=0.6(0.6)(0.5)
0.6P(AB)=0.60.3
0.6P(AB)=0.3
P(AB)=0.60.3
P(AB)=0.3
Therefore, the probability that both the man and his wife are alive after 50 years and one of them is dead is 0.3 or 30%.

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