Question

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?

Answer 1

• 1/33

Step-by-step 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