To find the probability that a marble selected at random from the bag is either green or red, we first need to determine the total number of marbles and the number of marbles that are green or red.
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Total number of marbles:
- Green marbles: 3
- Yellow marbles: 2
- Red marbles: 5
Therefore, the total number of marbles is: \[ 3 + 2 + 5 = 10 \]
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Number of favorable outcomes (green or red marbles):
- Green marbles: 3
- Red marbles: 5
Thus, the total number of green or red marbles is: \[ 3 + 5 = 8 \]
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Calculating the probability: The probability \( P \) of selecting a green or red marble is given by the ratio of the number of favorable outcomes to the total number of outcomes: \[ P(\text{green or red}) = \frac{\text{Number of green or red marbles}}{\text{Total number of marbles}} = \frac{8}{10} \]
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Simplifying the fraction: \[ \frac{8}{10} = \frac{4}{5} \]
Therefore, the probability that the marble selected is green or red is \(\frac{4}{5}\).