Chapter 12.5, Problem 1CYU

To determine

To state whether the probability is dependent or independent and find the probability.

Answer to Problem 1CYU

The events are dependent and the probability of choosing two stuffed animals are $\frac{28}{253}\text{ or 11\%}$ .

Explanation of Solution

Given information:

The given statement is:

“A toy bin contains $12$ toys, $8$ stuffed animals and $3$ board games. Marsha randomly chooses $2$ items for the child she is babysitting. What is the probability that she chooses $2$ stuffed animals as the first two choices?”

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The outcome of one event affects the outcome of the other because the stuffed animal is not replaced, so they are dependent events.

The probability that she chooses $2$ stuffed animals as the first two choice can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{one stuffed animal}\right)=\frac{8}{23}\\ \text{P}\left(\text{another stuffed animal}\right)=\frac{7}{22}\\ \text{P}\left(\text{two stuffed animals}\right)=\frac{8}{23}\times \frac{7}{22}\\ \text{P}\left(\text{two stuffed animals}\right)=\frac{28}{253}\text{ or 11\%}\end{array}$

Hence, the events are dependent and the probability of choosing two stuffed animals are $\frac{28}{253}\text{ or 11\%}$ .