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 at least one of them will be alive 20 years hence.

• A. $\frac{61}{96}$
• B. $\frac{31}{96}$
• C. $\frac{41}{70}$
• D. $Noneofthese$

Answer 1

The correct option is A $\frac{61}{96}$

P(atleasr one of them will be alive 20 years hence)
= 1 - P(none will be alive 20 years hence)
$=1-P(\overline{E}\cup \overline{F})$
$=1-p\left(\overline{E}\right)P\left(\overline{F}\right)(\therefore \overline{E}and\overline{F}$ independent)
$=1-(\frac{7}{12}\times \frac{5}{8})=\frac{61}{96}$