Conditional probability involves the idea that with extra knowledge of a situation, the likelihood of a given outcome can change. Consider the following premise:<\/p>\n
Example 1<\/strong><\/p>\n At ABC Insurance, the general likelihood of living past age 75 is 41%. What is Herbert’s likelihood of living past 75, given<\/p>\n a)that he is age 30?<\/p>\n b)that he is age 80?<\/p>\n Solution<\/strong>:<\/p>\n For question a), at age 30, Herbert likely still has about 41% probability of living past 75.<\/p>\n In the case of b), at age 80, Herbert has 100% probability of surviving past age 75: he has already done it.<\/p>\n The formula for the conditional probability of Event X given Event Y, P(X|Y), is<\/p>\n P(X|Y)=P(Y and X)\/P(Y)<\/p>\n For b) above, <\/p>\n P(Herbert lives past 75|he’s 80)=P(Herbert is 80 and past 75)\/P(Herbert is 80)<\/p>\n Of course, the probability Herbert is 80 and past 75 simply equals the probability he is 80: being 80, he’s inherently past 75.<\/p>\n Therefore,<\/p>\n P(Herbert lives past 75|he’s 80)=P(Herbert is 80)\/P(Herbert is 80)=1=100%<\/p>\n I’ll be giving further examples of conditional probability in future posts:)<\/p>\n Source:<\/p>\n Ross, Sheldon. A First Course in Probability<\/u>. New York: Macmillan, Inc., 1988.<\/p>\n