A) \[59/91\]
B) \[44/91\]
C) \[51/91\]
D) \[32/91\]
Correct Answer: B
Solution :
Probability [Person A will die in 30 years] \[=\frac{8}{8+5}\] \[P(A)=\frac{8}{13}\Rightarrow P(\bar{A})=\frac{5}{13}\] Similarly, \[P(B)=\frac{4}{7}\Rightarrow P(\bar{B})=\frac{3}{7}\] There are two ways in which one person is alive after 30 years. \[\bar{A}B\] and \[A\bar{B}\] and event are independent. So, required probability \[=P(\bar{A}).P(B)+P(A).P(\bar{B})=\frac{5}{13}\times \frac{4}{7}+\frac{8}{13}\times \frac{3}{7}=\frac{44}{91}.\]
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