The tutor wades into a case of conditional probability.

Conditional probability involves the idea that with extra knowledge of a situation, the likelihood of a given outcome can change. Consider the following premise:

Example 1

At ABC Insurance, the general likelihood of living past age 75 is 41%. What is Herbert’s likelihood of living past 75, given

a)that he is age 30?

b)that he is age 80?

Solution:

For question a), at age 30, Herbert likely still has about 41% probability of living past 75.

In the case of b), at age 80, Herbert has 100% probability of surviving past age 75: he has already done it.

The formula for the conditional probability of Event X given Event Y, P(X|Y), is

P(X|Y)=P(Y and X)/P(Y)

For b) above,

P(Herbert lives past 75|he’s 80)=P(Herbert is 80 and past 75)/P(Herbert is 80)

Of course, the probability Herbert is 80 and past 75 simply equals the probability he is 80: being 80, he’s inherently past 75.

Therefore,

P(Herbert lives past 75|he’s 80)=P(Herbert is 80)/P(Herbert is 80)=1=100%

I’ll be giving further examples of conditional probability in future posts:)

Source:

Ross, Sheldon. A First Course in Probability. New York: Macmillan, Inc., 1988.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.