  ### Home > CCG > Chapter 11 > Lesson 11.1.3 > Problem11-50

11-50.

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. Calculate the probability that a participant chose cracker A or was under $20$ years old. Show how you used the Addition Rule.

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

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

$46.9$%

2. What is the probability that a participant did not choose cracker A and was over $20$ years old? Show how you used a complement to answer this problem.

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

3. What is the probability that a participant was $20$ years old or older. Show how you used a complement to answer this problem.

Use the same method from part (b).

4. 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.

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

$60.8$%