A bag contains 14 green, 12 orange, and 19 purple tennis balls. a. Create a probability model for choosing a tennis ball from the bag. b. Suppose a tennis ball is randomly selected and then replaced 75 times. How many orange tennis balls do you expect?

1. Problem Description

A bag contains 14 green, 12 orange, and 19 purple tennis balls.

a. Create a probability model for choosing a tennis ball from the bag.

b. Suppose a tennis ball is randomly selected and then replaced 75 times. How many orange tennis balls do you expect?

2. Solution Steps

a.

First, find the total number of tennis balls in the bag:

$14 + 12 + 19 = 45$

The probability of choosing a green tennis ball is:

$P(Green) = \frac{14}{45}$

The probability of choosing an orange tennis ball is:

$P(Orange) = \frac{12}{45} = \frac{4}{15}$

The probability of choosing a purple tennis ball is:

$P(Purple) = \frac{19}{45}$

The probability model is:

Green: $\frac{14}{45}$

Orange: $\frac{12}{45}$

Purple: $\frac{19}{45}$

b.

A tennis ball is selected randomly and replaced 75 times.

The probability of choosing an orange tennis ball is $\frac{12}{45} = \frac{4}{15}$.

The expected number of orange tennis balls is:

$75 \times P(Orange) = 75 \times \frac{12}{45} = 75 \times \frac{4}{15} = 5 \times 4 = 20$

3. Final Answer

a.

The probability model is:

Green: $\frac{14}{45}$

Orange: $\frac{12}{45}$

Purple: $\frac{19}{45}$

b.

We expect 20 orange tennis balls.