Question

the probability that a man will be alive in 25 years is 3/5 and probability for his wife in 25 year is 2/3. find probability that
a) both will be alive in 25 years
b) only the wife will be alive in 25 years

Answer 1

Question #13683

the probability that a man will be alive in 25 years is $3/5$ and probability for his wife in 25 years is $2/3$. find probability that a) both will be alive in 25 years b) only the wife will be alive in 25 years

Solution. Denote by $M$ the event that man will be alive in 25 years, $W$ — the wife will be alive in 25 years. Then $M$ and $W$ are independent and $P(M) = 3/5$ and $P(W) = 2/3$. Now we are to find a) $P(M \cap W) = 3/52/3 = 2/5$ and b) $P(W \cap \overline{M}) = 2/32/5 = 4/15$.

Answer. a) $2/5$. b) $4/15$.