Exercise 123 Page 206

a To determine probability, we divide the number of favorable outcomes by the number of possible outcomes.

P=Number of favorable outcomes/Number of possible outcomes The total number of fruits (possible outcomes) that the ice chest can hold is 18. We want to find the number of carrots (favorable outcomes), which we can call x, that we need for the probability of picking a carrot to be 40 %.

P=Number of favorable outcomes/Number of possible outcomes

SubstituteValues

Substitute values

0.4=x/18

MultEqn

LHS * 18=RHS* 18

7.2=x

RearrangeEqn

Rearrange equation

x=7.2

RoundInt

Round to nearest integer

x≈ 7

The number of carrots should be 7. With that said, for the probability to be exactly 40 %, we need 7.2 carrots. This is however not possible as we are only counting whole carrots.

b From the exercise, we know that the chest contains 2 red apples, 5 apricots, 1 mango, 2 red tomatoes, 1 red grapefruit, 4 bananas, 2 nectarines and 1 peach. If we add the number of fruits, we get the total number of possible outcomes.

2+5+1+2+1+4+2+1=18 We are looking for the probability of picking a red fruit or vegetable. From the list of items, the apples, tomatoes and grapefruit are red. This means we have 2+2+1=5 favorable outcomes. Now we can calculate the probability of picking a red piece.

P=Number of favorable outcomes/Number of possible outcomes

SubstituteValues

Substitute values

P(red piece)=5/18

CalcQuot

Calculate quotient

P(red piece)=0.27777...

RoundDec

Round to 3 decimal place(s)

P(red piece)≈ 0.278

WritePercent

Convert to percent

P(red piece)≈ 27.8 %

The probability of picking a red piece is about 27.8 %.

c By adding pomegranates, the number of possible outcomes increases by 7.

18+7=25 The number of possible outcomes is 25 and the number of favorable outcomes, the pomegranates, are 7. With this, we can calculate the probability of picking a pomegranate.

P=Number of favorable outcomes/Number of possible outcomes

SubstituteValues

Substitute values

P(pomegranate)=7/25

CalcQuot

Calculate quotient

P(pomegranate)=0.28

WritePercent

Convert to percent

P(pomegranate)=28 %

The probability of picking a pomegranate is 28 %.