Question

For a 60 years old person living upto the age of 70, it is 7:5 against him and for another 70 years old person surviving upto the age of 80, it is 5:2 against him. The probability that only one of them will survive for 10 years more is ______.

• A. 15/42
• B. 39/84
• C. 49/84
• D. 40/84

Answer 1

The correct option is B 39/84

$Let{E}_1,E_{2}o\text{f survival of A and B respectively}$
$\text{Way in which one of them survive:}$
$\text{i)A survives and B dies}$
$\text{ii)A dies and B survives}$
$\text{Required probability=}\frac{5}{12}\times \frac{5}{7}+\frac{2}{7}\times \frac{7}{12}$
$=\frac{25}{84}+\frac{14}{84}$
$=\frac{39}{84}$