To find the probability of picking a red or a green marble from the bag, we first need to determine the total number of marbles.
The bag contains:
- 3 blue marbles
- 4 red marbles
- 2 green marbles
Calculating the total number of marbles: \[ \text{Total marbles} = 3 \text{ (blue)} + 4 \text{ (red)} + 2 \text{ (green)} = 9 \text{ marbles} \]
Next, we count the number of favorable outcomes for picking a red or a green marble. The number of red marbles is 4, and the number of green marbles is 2.
Adding these together gives: \[ \text{Number of red or green marbles} = 4 \text{ (red)} + 2 \text{ (green)} = 6 \]
Now, we can compute the probability of picking either a red or a green marble using the formula for probability: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{9} \]
To simplify this fraction: \[ \frac{6}{9} = \frac{2}{3} \]
Thus, the probability of picking a red or a green marble is \(\frac{2}{3}\).