Exercise 145 Page 336

a Kayla will choose three different snacks, and we need to calculate their respective probabilities. To do that we have to identify the number of favorable outcomes and the number of possible outcomes for each type of flavored water, fruit and crackers.

Flavored Water

Kayla packed two types of flavored water: berry and citrus. Of these, 2 bottles were berry flavored and 4 bottles were citrus flavored for a total of 6 bottles. P(berry)&=2/6 [1.2em] P(citrus)&=4/6

Fruit

Kayla also packed three types of fruit: apricots, apples, and grapes. Of these, 5 were apricots, 2 were apples, and 3 were grapes for a total of 10 pieces of fruit. P(apricots)&=5/10 [1em] P(apples)&=2/10 [1em] P(grapes)&=3/10

Crackers

Finally, Kayla brought two different types of crackers. Of these, 2 were regular and 2 were whole-wheat for a total of 4 crackers. P(regular)&=2/4 [1em] P(whole wheat)&=2/4

Tree Diagram

Having calculated the probabilities of picking the different kinds of flavored water, fruit and crackers, we can draw a tree diagram illustrating all of the possible combinations.

b Let's highlight all of the combinations that give you a high-fiber snack. That is a combination that includes both an apple and a whole-wheat creacker.

To determine the probability of a certain combination, we have to multiply all of the probabilities that are included in this combination. P(berry,apple,wheat): 2/6* 2/10* 2/4=8/240 [0.8em] P(citrus,apple,wheat): 4/6* 2/10* 2/4=16/240 Finally, to get the probability of choosing either of these combinations we have to add the probabilities.

P(berry,apple,wheat)+P(citrus,apple,wheat)

SubstituteValues

Substitute values

8/240+16/240

AddFrac

Add fractions

24/240

ReduceFrac

a/b=.a /24./.b /24.

1/10

WritePercent

Convert to percent