Question

The present age of a person A is 35. The odds in favour of his living upto the age of 65 is 3:2. The age of another person B is 40 at present. The odds against his living upto the age 70 is 4:1. The probability that at least one of them will be alive after 30 years is _____.

• A. 17/30
• B. 17/25
• C. 18/72
• D. 7/25

Answer 1

The correct option is B 17/25

$Given:$
$P\left(A\right)=\frac{3}{5}$
$P\left(B\right)=\frac{1}{5}$
$P(A\cup B)=1-P\left(\overline{A}\right)P\left(\overline{B}\right)$
$=1-(1-\frac{3}{5})(1-\frac{1}{5})$
$=1-\left(\frac{2}{5}\right)\left(\frac{4}{5}\right)$
$=\frac{17}{25}$