Question

Suppose that, it is odds against a person who is now 40 years of age living till he is 75, 5 : 3 and against B now 35 living till he is 70 is 5 : 3, find the chance that at least one of these persons will be alive 35 years hence.

Answer 1

Let E1 be the event that man A will be alive 35 years hence

E2 is the event if person B will be alive 35 years hence

So,

p(E1)=3/8

and p(E2) =3/8

So
$p(\bar E1) = (1 - \frac{3}{8} ) = \frac{5}{8} \\ \\ p(\bar E2) = (1 - \frac{3}{8} ) = \frac{5}{8}$
it is clear that both the events are independent

So, to find the chance that at least one of these persons will be alive 35 years hence

$p(at \: least \: one \: of \: them \: will \: be \: alive \: 35 \: years \: hence) \\ \\ = 1 - p(none \: will \: be \: alive) \\ \\ = 1 -[ p(\bar E1).p(\bar E2)] \\ \\ = 1 - [\frac{5}{8} \times \frac{5}{8} ]\\ \\ = 1 - \frac{25}{64} \\ \\ = \frac{39}{64}$
Hope it helps you