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. 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).

P(AandB)=P(A)* P(BfollowingA)

SubstituteII

P(A)= 8/23, P(BfollowingA)= 7/22

P(AandB)= 8/23* 7/22

▼

Simplify right-hand side

SplitIntoFactors

Split into factors

P(AandB)=2*4/23 * 7/2* 11

CancelCommonFac

Cancel out common factors

P(AandB)=2*4/23 * 7/2* 11

SimpQuot

Simplify quotient

P(AandB)=4/23 * 7/11

MultFrac

Multiply fractions

P(AandB)=28/253

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.

P(AandB)=28/253

UseCalc

Use a calculator

P(AandB)=0.110672...

RoundDec

Round to 2 decimal place(s)

P(AandB)≈ 0.11

WritePercent

Convert to percent

P(AandB)≈ 11 %

The probability is about 11 %.