To determine which bags provide a good model for a probability of pulling a blue marble of 0.25, we need to calculate the probability of picking a blue marble from each bag.
The formula for probability is:
\[ P(\text{blue}) = \frac{\text{number of blue marbles}}{\text{total number of marbles}} \]
Now let's calculate the probabilities for each of the options:
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10 yellow, 3 red, 10 blue:
- Total marbles = 10 + 3 + 10 = 23
- Probability \( P(\text{blue}) = \frac{10}{23} \approx 0.4348 \) (not a good model)
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5 yellow, 9 red, 3 blue:
- Total marbles = 5 + 9 + 3 = 17
- Probability \( P(\text{blue}) = \frac{3}{17} \approx 0.1765 \) (not a good model)
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1 yellow, 2 red, 3 blue, 5 green, 1 purple:
- Total marbles = 1 + 2 + 3 + 5 + 1 = 12
- Probability \( P(\text{blue}) = \frac{3}{12} = 0.25 \) (this is a good model)
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6 yellow, 5 red, 10 blue, 12 green, 7 purple:
- Total marbles = 6 + 5 + 10 + 12 + 7 = 40
- Probability \( P(\text{blue}) = \frac{10}{40} = 0.25 \) (this is also a good model)
Good models for the probability of pulling a blue marble of 0.25:
- 1 yellow, 2 red, 3 blue, 5 green, 1 purple
- 6 yellow, 5 red, 10 blue, 12 green, 7 purple