To determine which bags of marbles are good models for the probability of pulling a blue marble with a probability of 0.25, we need to check if the ratio of blue marbles to the total number of marbles in each bag yields a probability of 0.25.
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For the bag with 1 yellow, 2 red, 3 blue, 5 green, 1 purple:
- Total marbles = 1 + 2 + 3 + 5 + 1 = 12
- Probability of blue = 3 blue / 12 total = 0.25
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For the bag with 5 yellow, 9 red, 3 blue:
- Total marbles = 5 + 9 + 3 = 17
- Probability of blue = 3 blue / 17 total ≈ 0.176 (not 0.25)
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For the bag with 6 yellow, 5 red, 10 blue, 12 green, 7 purple:
- Total marbles = 6 + 5 + 10 + 12 + 7 = 40
- Probability of blue = 10 blue / 40 total = 0.25
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For the bag with 10 yellow, 3 red, 10 blue:
- Total marbles = 10 + 3 + 10 = 23
- Probability of blue = 10 blue / 23 total ≈ 0.435 (not 0.25)
Based on this, the bags that yield a probability of pulling a blue marble equal to 0.25 are:
- Bag 1: 1 yellow, 2 red, 3 blue, 5 green, 1 purple
- Bag 3: 6 yellow, 5 red, 10 blue, 12 green, 7 purple
Thus, the correct responses are the first and third bags.