Q.The odds against a husband who is 60 years old, living till he is 85 are 7:5. The odds against his wife who is now 56, living till she is 81 are 5:3. Find the probability that a) at least one of them will be alive 25 years hence b) exactly one of them will be alive 25 years hence.

Odds against husband alive $7:5$ gives $P(\text{husband alive})=5/12$. Odds against wife alive $5:3$ gives $P(\text{wife alive})=3/8$.

a) At least one alive $=1-P(\text{neither})=1-(1-\frac{5}{12})(1-\frac{3}{8})=1-\frac{7}{12}\times\frac{5}{8}=1-\frac{35}{96}=\frac{61}{96}$. …

Convert odds against to survival probabilities, then combine via independence as in the ear …

Converting 'odds against living' incorrectly to mean the probability of NOT living, when the second number in th …