To determine the likelihood that Jessica will draw a green marble after first drawing 2 blue marbles and 1 red marble from the bag, we'll first analyze the situation based on the contents of the bag after these draws.
Initially, the bag contains the following marbles:
- Blue: 5
- Red: 3
- Green: 4
- Total: 12 marbles
After drawing 2 blue marbles and 1 red marble, the count of marbles in the bag will be:
- Blue: \(5 - 2 = 3\)
- Red: \(3 - 1 = 2\)
- Green: 4 (unchanged)
- Total marbles remaining: \(12 - 3 = 9\)
Now, we want to find the likelihood that the next marble drawn is green. There are 4 green marbles remaining and a total of 9 marbles in the bag.
The probability of drawing a green marble now is given by: \[ \text{Probability of drawing a green marble} = \frac{\text{Number of green marbles}}{\text{Total number of remaining marbles}} = \frac{4}{9} \]
Therefore, the answer is: 4 ninths