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

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2
. Which of the following can be the contents of the box?

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

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

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

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

1 answer

To find which option meets the probability condition provided by Carlos, we need to determine the total number of bags in each scenario and calculate the probability of selecting a bag of potato chips.

The probability of selecting a bag of potato chips is given as \( \frac{1}{2} \). This means that the number of bags of potato chips must equal half of the total number of bags.

Let's evaluate each option:

A. 4 bags of potato chips and 8 bags of pretzels:

  • Total bags = \( 4 + 8 = 12 \)
  • Probability of potato chips = \( \frac{4}{12} = \frac{1}{3} \) (not \( \frac{1}{2} \))

B. 8 bags of potato chips and 8 bags of pretzels:

  • Total bags = \( 8 + 8 = 16 \)
  • Probability of potato chips = \( \frac{8}{16} = \frac{1}{2} \) (this is correct)

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

  • Total bags = \( 10 + 5 = 15 \)
  • Probability of potato chips = \( \frac{10}{15} = \frac{2}{3} \) (not \( \frac{1}{2} \))

D. 5 bags of potato chips and 10 bags of pretzels:

  • Total bags = \( 5 + 10 = 15 \)
  • Probability of potato chips = \( \frac{5}{15} = \frac{1}{3} \) (not \( \frac{1}{2} \))

The only option that results in a \( \frac{1}{2} \) probability of selecting a bag of potato chips is:

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