The event of choosing the first stuffed animal affects the probability of drawing the second one. Therefore, the events are dependent.
Independent or dependent: Dependent Probability: 28253 or about 11 %
Practice makes perfect
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.
P(AandB)=P(A)* P(BfollowingA)
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.
P(stuffed animal)&=8/23 l←number of stuffed animals ←number of items
Let's call the event of choosing a stuffed animal as the second item B. Then P(BfollowingA) is the probability of choosing a stuffed animal, given that the first item chosen is a stuffed animal. Since Marsha has already chosen a stuffed animal, there are 22 items remaining in the bin, from which 7 are stuffed animals.
P(BfollowingA)&= 7/22 l←number ofremainingstuffed animals ←number ofremainingitems
Finally, according to the formula, to calculate P(Aand B) we have to multiply P(A) and P(BfollowingA).
We have found that the probability of choosing two stuffed animals as the first two choices is 28253. We can also write this probability as a percentage.
