Exercise 1 Page 797

The event of choosing the first stuffed animal affects the probability of choosing the second one. This is because there is one fewer item in the bin from which to choose, and one fewer stuffed animal to choose. Thus, the events are dependent.

Probability of Dependent Events

If two events $A$ and $B$ are dependent, then the probability that A and B will occur is the product of the probability of $A$ and the probability of $B$ after $A$ has occured. $$\begin{array}{c}P(A\text{ and }B)=P(A)\cdot P(B\text{ following }A)\end{array}$$

Let's call the event of choosing a stuffed animal as the first item $A.$ We'll first calculate the probability of choosing a stuffed animal from the toy bin, $P(A).$ The bin contains $12$ toys, $8$ stuffed animals and $3$ board games, which makes a total of $23$ items, $8$ of which are stuffed animals.