Question

Carlos has a box containing bags of potato chips and pretzels. He told Sarah that the probability that she randomly selects a bag of potato chips is
1
2
. Which of the following can be the contents of the box?

A.
8 bags of potato chips and 8 bags of pretzels

B.
5 bags of potato chips and 10 bags of pretzels

C.
10 bags of potato chips and 5 bags of pretzels

D.
4 bags of potato chips and 8 bags of pretzels

Answer 1

To determine which option can result in the given probability of selecting a bag of potato chips being \( \frac{1}{2} \), we need to check if the ratio of the number of bags of potato chips to the total number of bags (potato chips + pretzels) equals \( \frac{1}{2} \).

**Let's analyze each option:**

A. **8 bags of potato chips and 8 bags of pretzels:**
- Total bags = \( 8 + 8 = 16 \)
- Probability of selecting potato chips = \( \frac{8}{16} = \frac{1}{2} \)
- This option is valid.

B. **5 bags of potato chips and 10 bags of pretzels:**
- Total bags = \( 5 + 10 = 15 \)
- Probability of selecting potato chips = \( \frac{5}{15} = \frac{1}{3} \)
- This option is not valid.

C. **10 bags of potato chips and 5 bags of pretzels:**
- Total bags = \( 10 + 5 = 15 \)
- Probability of selecting potato chips = \( \frac{10}{15} = \frac{2}{3} \)
- This option is not valid.

D. **4 bags of potato chips and 8 bags of pretzels:**
- Total bags = \( 4 + 8 = 12 \)
- Probability of selecting potato chips = \( \frac{4}{12} = \frac{1}{3} \)
- This option is not valid.

**Conclusion:**
The only option that gives a probability of selecting a bag of potato chips as \( \frac{1}{2} \) is:

**A. 8 bags of potato chips and 8 bags of pretzels.**