Question

name introduction to probability & fundamental counting principle class cp algebra 2 use the candy box to solve each problem. 1) how many total pieces of candy are in the box? 2) what is the probability of selecting a cherry piece? 3) what is the probability of selecting a lemon piece? 4) what is the probability of selecting a grape piece? 5) if you picked 1 piece of candy out of the box, which flavor would you have the highest probability of selecting? 6) which flavor has the lowest probability of being selected? 7) what is the probability of not selecting a cherry piece? 8) what is the probability of selecting a strawberry piece? 9) what is the probability of selecting a grape, cherry, or lemon piece?

Explanation:

Step1: Count total candies

Count all candies in the box. There are 12 candies.

Step2: Calculate probability of cherry

There are 3 cherry - flavored candies. Probability = $\frac{\text{Number of cherry candies}}{\text{Total number of candies}}=\frac{3}{12}=\frac{1}{4}$.

Step3: Calculate probability of lemon

There are 5 lemon - flavored candies. Probability = $\frac{5}{12}$.

Step4: Calculate probability of grape

There are 4 grape - flavored candies. Probability = $\frac{4}{12}=\frac{1}{3}$.

Step5: Determine highest - probability flavor

Compare probabilities: $\frac{1}{4}$ (cherry), $\frac{5}{12}$ (lemon), $\frac{1}{3}$ (grape). Since $\frac{5}{12}>\frac{1}{3}>\frac{1}{4}$, lemon has the highest probability.

Step6: Determine lowest - probability flavor

Cherry has the lowest probability among the three flavors as $\frac{1}{4}<\frac{1}{3}<\frac{5}{12}$.

Step7: Calculate probability of not cherry

Probability of not cherry = 1 - Probability of cherry = $1-\frac{1}{4}=\frac{3}{4}$.

Step8: Calculate probability of strawberry

There are 0 strawberry - flavored candies. Probability = $\frac{0}{12}=0$.

Step9: Calculate probability of grape, cherry, or lemon

Since all candies in the box are grape, cherry, or lemon, probability = $\frac{12}{12}=1$.

Answer:

1. 12
2. $\frac{1}{4}$
3. $\frac{5}{12}$
4. $\frac{1}{3}$
5. Lemon
6. Cherry
7. $\frac{3}{4}$
8. 0
9. 1