Question

Suppose a jar contains 9 red marbles and 15 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

`(3)/(23)`

Explanation:

Since we start with 24 marbles, 9 of which are red, the probability of selecting a red marble is 9/24. The red marble is not put back, so there are now 23 marbles, 8 of which are red. It follows that the probability of selecting a second red marble is 8/23. So the probability of selecting a red marble and then another red marble is

`(9)/(24) * (8)/(23) = (3)/(8) * (8)/(23) = (3)/(23)`