Suppose a jar contains 10 red marbles and 27 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

Here are two suggestions:

Approach #1: The event "both are red" is the same as the event "the first marble is red AND the second marble is red". But drawing marbles at the same time is the same as drawing without replacement. So use the multiplication rule for DEPENDENT events: P(A and B)=P(A)*P(B|A) where A="first marble is red" and B="second marble is red".

Approach #2: The problem describes a hypergeometric probability with parameters N=37, K=10, n=2, and k=2. Use the hypergeometric pmf to compute the desired probability. If you forget the hypergeometric pmf, it's easy to look up on wikipedia under "hypergeometric distribution".

Whichever approach you take, there answer should be the same.