Sure, let's solve this step-by-step.
Initially, the bag contains:
- 2 orange marbles
- 3 black marbles
- 5 pink marbles
When one pink marble is drawn and not replaced, the remaining marbles in the bag are:
- 2 orange marbles
- 3 black marbles
- 4 pink marbles (since 1 pink marble was drawn out of the original 5)
Let's now determine the total number of marbles left in the bag:
[tex]\[ \text{Total marbles remaining} = 2 \, (\text{orange}) + 3 \, (\text{black}) + 4 \, (\text{pink}) = 9 \][/tex]
Next, we need to find the probability of drawing a pink marble from the remaining marbles. The probability can be calculated using the formula for probability:
[tex]\[ P(\text{drawing a pink marble}) = \frac{\text{Number of pink marbles}}{\text{Total number of marbles}} \][/tex]
Substituting the values we have:
[tex]\[ P(\text{drawing a pink marble}) = \frac{4}{9} \][/tex]
Thus, the probability of drawing a pink marble next is \(\frac{4}{9}\).
Therefore, the correct answer is:
B) [tex]\(\frac{4}{9}\)[/tex]
