To find the probability of picking either a green or a red marble from the bag, we first need to determine the total number of marbles in the bag and the number of favorable outcomes (green and red marbles).
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Count the marbles by color:
- Blue marbles: 8
- Red marbles: 24
- Green marbles: 16
- Yellow marbles: 4
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Calculate the total number of marbles: \[ \text{Total number of marbles} = 8 + 24 + 16 + 4 = 52 \]
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Calculate the number of favorable outcomes (green and red marbles): \[ \text{Number of green marbles} = 16 \] \[ \text{Number of red marbles} = 24 \] \[ \text{Total favorable outcomes} = 16 + 24 = 40 \]
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Calculate the probability of picking either a green or a red marble: \[ P(\text{green or red}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of marbles}} = \frac{40}{52} \]
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Simplify the fraction: \[ \frac{40}{52} = \frac{10}{13} \]
Thus, the probability of picking either a green or a red marble is \(\frac{10}{13}\).