Question

Suppose that the overall probability of living to age 70 is 0.62 and that the overall probability of living to age 80 is 0.23. If a person reaches their 70th birthday, what is the probability that they will live to age 80?

Answer 1

Given :

P( X = 70 ) = 0.62 .

P( X = 80 ) = 0.23 .

To Find :

We need to find If a person reaches their 70th birthday, what is the probability that they will live to age 80 .

Solution :

We need to find :

$P(X=70 | X=80 )$

We know ,

$P(x,y ) = \dfrac{P(x)}{P(y)}$

So ,

$P(X=70 | X=80 )=\dfrac{P(X=80)}{P(X=70)}\\\\=\dfrac{0.62}{0.23}=0.371$

Hence , this is the required solution .