Answer to Question #322483 in Statistics and Probability for Asma

Question

The probability that the man will be alive 25 years is 2/3 and the probability that his wife will be alive 25 years 2/3.find the probability that:

both will be alive

Answer 1

Let,  M = the event that the man will be alive in 25 years, and

W = the event that his wife will be alive in 25 years.

We are said that $P(M) =\cfrac{2} {3} , \ P(W) =\cfrac{2} {3}.$

Observe that, M and W are independent events , so

$P(M\cap W) =P(M) \cdot P(W) =\cfrac{2} {3}\cdot \cfrac{2} {3}=\cfrac{4} {9}.$