Sure, let's go through the step-by-step solution for each of the probabilities from the given scenario.
### Step 1: Determine the Total Number of Candies
First, calculate the total number of miniature candy bars in the bag:
- Crunch: 15 bars
- Hershey's Chocolate: 14 bars
- Mr. Goodbar: 10 bars
- Cookies and Cream: 12 bars
Add these quantities together to get the total:
[tex]\[ 15 + 14 + 10 + 12 = 51 \][/tex]
So, there are 51 candies in total.
### Step 2: Calculate Each Probability
1. Probability of randomly choosing a Crunch bar ([tex]\(P(R)\)[/tex]):
We know there are 15 Crunch bars out of a total of 51 candies. So, the probability [tex]\(P(R)\)[/tex] is the number of Crunch bars divided by the total number of candies:
[tex]\[ P(R) = \frac{15}{51} \][/tex]
2. Probability of randomly choosing a Mr. Goodbar ([tex]\(P(G)\)[/tex]):
There are 10 Mr. Goodbars in the bag. The probability [tex]\(P(G)\)[/tex] is the number of Mr. Goodbars divided by the total number of candies:
[tex]\[ P(G) = \frac{10}{51} \][/tex]
3. Probability of randomly choosing a Cookies and Cream bar ([tex]\(P(K)\)[/tex]):
There are 12 Hershey's Cookies and Cream bars. The probability [tex]\(P(K)\)[/tex] is the number of Cookies and Cream bars divided by the total number of candies:
[tex]\[ P(K) = \frac{12}{51} \][/tex]
### Step 3: Represent Each Probability as a Reduced Fraction
- Probability of Crunch bar ([tex]\(P(R)\)[/tex]):
[tex]\[ P(R) = \frac{15}{51} \][/tex]
- Probability of Mr. Goodbar ([tex]\(P(G)\)[/tex]):
[tex]\[ P(G) = \frac{10}{51} \][/tex]
- Probability of Cookies and Cream bar ([tex]\(P(K)\)[/tex]):
[tex]\[ P(K) = \frac{12}{51} \][/tex]
So, the probabilities are as follows:
1. [tex]\(P(R) = \frac{15}{51}\)[/tex]
2. [tex]\(P(G) = \frac{10}{51}\)[/tex]
3. [tex]\(P(K) = \frac{12}{51}\)[/tex]
