Question

Odds 8 to 5 against a person who is 40 years old living till he is 70 and 4 to 3 against another person now 50 till he will be living 80. Probability that one of them will be alive next 30 years.

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Probability [Person A will die in 30 years] = $\frac{8}{8+5}$
P(A) = $\frac{8}{13}\Rightarrow$ $P\left(\overline{A}\right)=\frac{5}{13}$
Similarly, P(B) = $\frac{4}{7}$ $\Rightarrow$ $P\left(\overline{B}\right)=\frac{3}{7}$
Therefore are two ways in which one person is alive after 30 years. $\overline{A}B$ and $A\overline{B}$ and event are independent.
So, required probability
$=P\left(\overline{A}\right).P\left(B\right)+P\left(A\right).P\left(\overline{B}\right)=\frac{5}{13}\times \frac{4}{7}+\frac{8}{13}\times \frac{3}{7}=\frac{44}{91}$