  ### Home > INT2 > Chapter 9 > Lesson 9.2.2 > Problem9-72

9-72.

A snack cracker company conducted a taste test for the three different types of crackers it makes. It surveyed $250$ people in each age group in the table below. Participants chose their favorite type of cracker. Use the results to answer the questions.

Age

Cracker A

Cracker B

Cracker C

Under 20

$152$

$54$

$44$

20 to 39

$107$

$85$

$58$

40 to 59

$78$

$101$

$71$

60 and over

$34$

$68$

$148$

1. What is the probability that a participant chose cracker A or was under $20$ years old? Use the Addition Rule.

If the question says 'or' you must subtract the probability of 'and'.

$P\left(\text{cracker A}\right) + P\left(\text{under } 20\right) − P\left(\text{cracker A and under } 20 \right)$

$46.9\%$

1. What is the probability that a participant did not choose cracker A and was over $20$ years old? Use a complement to answer this question.

To use the complement, reverse the method you used in part (a).
Subtract P(cracker A) and P(Under $20$) from the total.

2. What is the probability that a participant was $20$ years old or older? Use a complement to answer this question.

Use the same method from part (b).

3. A randomly-selected participant says he is $15$ years old. What is the probability that he chose cracker A?

Each age group only has $250$ participants.

$\frac{ \# \: \text{of participants under 20 who picked cracker A}} {\# \: \text{participants in age group}}$

$60.8\%$