A bag of gumballs contains 2 pink, 3 orange, 4 blue, 2 red,

and 1 yellow gumballs. Pierre selects two gumballs from the

bag, without replacement. What is the probability that Pierre

selects a yellow and a pink gumball?

1/33

Explanation:

1. Sample space

The total number of gums is 2 + 3 + 4 + 2 + 1 = 12.

The number of different outcomes, i. e. the size of the sample space, for the selection of two gumballs from 12 gums is 12 * 11 = 132 different combinations.

2. Number of combinations for the desired outocome.

There are four possible combinations in which one ball is pink and one is yellow:

first is yellow and second is one of the pinks first is yellow and second is the other pink first is one of the pinks and second is yellow first is the other pink and second is yellow

3. Probability

By definition:

Probability = number of favorable outcomes / total number of outcomes

Therefore:

Probability that Pierre selects a yellow and a pink gumball = 4/132

Probability that Pierre selects a yellow and a pink gumball = 1/33