Example. Suppose that the sample space is the population of adults in a small town who have completed the requirements for a college degree. We categorize them according to sex and employment status as shown. Now one individual is to be selected at random. Find P(E), P(M) and P( M | E ).
Definition: P( M | E ) = P( M and E ) / P( E ).
Multiplication Rule:
P( A and B ) = P( A )* P( B | A ) = P( B )* P( A | B )
Example. Two cards are drawn in succession from a deck without replacement. What is the probability that both cards are hearts?
Solution. (13/52)*(12/51).