Exercise 149 Page 337

a Probability is calculated by dividing the number of favorable outcomes with the total number of outcomes.

P=Number of favorable outcomes/Number of possible outcomes People that are 20 years or older are represented by the people in the three last age brackets of the first table.

	Under 20	20 to 39	40 to 59	60 and over
# people	250	250 ✓	250 ✓	250 ✓

By adding the number of participants in the checkmarked age brackets, we can find the number of favorable outcomes. 250+250+250=750 Now we can calculate the probability of selecting a participant that is 20 years old or older.

P=Number of favorable outcomes/Number of possible outcomes

SubstituteValues

Substitute values

P(20 or older)=750/1000

CalcQuot

Calculate quotient

P(20 or older)=0.75

WritePercent

Convert to percent

P(20 or older)=75 %

b The probability of the union of two events A and B happening can be found using the Addition Rule.

P(A or B) =P(A)+P(B)-P(A and B) The probability of selecting a participant that chose Cracker A is 3711000, and the probability of selecting a participant that is under 20 years old is 2501000. Finally, we have to find the intersection of P(A) and P(B). From the exercise we know that 152 participants were both under 20 years old and chose Cracker A, which equals a probability of 1521000.

P(A or B) =P(A)+P(B)-P(A and B)

SubstituteValues

Substitute values

P(Cracker A or Under 20) = 371/1000+250/1000-152/1000

AddSubFrac

Add and subtract fractions

P(Cracker A or Under 20) = 371+250-152/1000

AddSubTerms

Add and subtract terms

P(Cracker A or Under 20) = 469/1000

CalcQuot

Calculate quotient

P(Cracker A or Under 20) = 0.469

WritePercent

Convert to percent

P(Cracker A or Under 20) = 46.9 %

c The probability that a participant did not choose Cracker A as their favorite and was 20 or over years old is the complement of the probability we calculated in Part B.

1-P(Cracker A or Under 20)

Substitute

P(Cracker A or Under 20)= 469/1000

1- 469/1000

OneToFrac

Rewrite 1 as 1000/1000

1000/1000-469/1000

SubFrac

Subtract fractions

531/1000

CalcQuot

Calculate quotient