Question

If Jessica is drawing marbles from a bag of 12 marbles (with 5 blue, 3 red, and 4
green marbles) and does not return them after each draw, then what is the
likelihood that she will draw a green marble after first drawing 2 blue marbles and 1
red marble?(1 point)
Responses

14
1
4
1 fourth

13
1
3
1 third

49
4
9
4 ninths

59

Answer 1

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**