Let's break down the solution to this problem step by step:
1. Initial Count of Marbles:
- White marbles: 3
- Orange marble: 1
- Green marbles: 2
Total initial marbles: \(3 + 1 + 2 = 6\)
2. Marble Drawn:
Anna draws a white marble. Since she does not replace it, we need to update our count:
- Drawn white marbles: 1
3. Remaining Marbles:
After Anna draws one white marble, the counts are as follows:
- White marbles: \(3 - 1 = 2\)
- Orange marble: 1 (no change)
- Green marbles: 2 (no change)
Total remaining marbles: \(2 + 1 + 2 = 5\)
4. Probability Calculation:
We are asked for the probability of drawing a green marble next. The count of remaining green marbles is 2, and the total remaining marbles is 5.
Therefore, the probability \(P\) of drawing a green marble is given by:
[tex]\[
P(\text{green marble}) = \frac{\text{number of green marbles}}{\text{total remaining marbles}} = \frac{2}{5}
\][/tex]
Thus, the probability of drawing a green marble next is \(\frac{2}{5}\).
So the correct answer is [tex]\( \boxed{\frac{2}{5}} \)[/tex].
