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A bag held 2 orange marbles, 3 black marbles, and 5 pink marbles. I drew a pink marble and did not replace it. What is the probability of drawing a pink marble next?

A) [tex]\frac{2}{5}[/tex]
B) [tex]\frac{4}{9}[/tex]
C) [tex]\frac{1}{2}[/tex]
D) [tex]\frac{5}{9}[/tex]

Sagot :

GinnyAnswer
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]
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