Question

The probability of Mr. A living 20 years more is 1/5 and that of Mr. B is 1/7. The probability that at least one of them will survive 20 years hence is ______.

• A. 12/35
• B. 1/35
• C. 11/35
• D. 14/35

Answer 1

Answer: (C)

11/35

$Let{E}_1,E_{2}o\text{f survival of A and B respectively}$
$\text{Way in which atleat one of them survive:}$
$\text{i)A survives and B dies}$
$\text{ii)A dies and B survives}$
$\text{iii) A and B survives}$
$\text{Required probability=}\frac{1}{5}\times \frac{6}{7}+\frac{4}{5}\times \frac{1}{7}+\frac{1}{5}\times \frac{1}{7}$
$=\frac{6}{35}+\frac{4}{35}+\frac{1}{35}$
$=\frac{11}{35}$