Question

The odds against a husband who is 50 years old living till he is 70 are 7:5 and the odds against his wife who is now 40, living till she is 60 are 5 : 3. Find the probability that the couple will be alive 20 years hence.

• A. $\frac{21}{32}$
• B. $\frac{5}{32}$
• C. $\frac{15}{32}$
• D. $\frac{12}{35}$

Answer 1

The correct option is B $\frac{5}{32}$

P (Couple will be alive 20 years hence)
$=P\left(EandF\right)=P(E\cap F)=P\left(E\right).P\left(F\right)=\frac{5}{12}\times \frac{3}{8}=\frac{5}{32}$