Question

Mary placed a bag containing one red ball, one blue ball, and one green ball on a table. She drew the three balls, one at a time, from the bag without looking. The list below shows all the possible combinations of the outcome.

RBG, RGB, BRG, BGR, GRB, GBR

Is Mary more likely to draw a red ball followed by a green ball or a blue ball among the first two balls to be drawn?

A. Mary is more likely to draw a red ball followed by a green ball, because 4/6 > 2/6

B. Mary is more likely to draw a blue ball among the first two balls to be drawn, because 4/6 > 2/6

C. Mary is more likely to draw a blue ball among the first two balls to be drawn, because 5/6 > 2/6

D. Mary is more likely to draw a red ball followed by a green ball, because 5/6 > 2/6

Answer 1

B. Mary is more likely to draw a blue ball among the first two balls to be drawn, because 4/6 > 2/6

Step-by-step explanation:

The probability of an event is the ratio of the number of ways that event can happen to the total number of possible outcomes. In this case, Mary is drawing three balls without looking, and there are six possible combinations of the outcome, as listed.

We need to determine whether Mary is more likely to draw a red ball followed by a green ball or a blue ball among the first two balls to be drawn. Let's consider each option separately.

•Option A: Mary is more likely to draw a red ball followed by a green ball, because 4/6 > 2/6

This option assumes that the probability of drawing a red ball followed by a green ball is 4/6, or two-thirds. However, there are only two ways to get this outcome: RBG and GRB. So, the probability of drawing a red ball followed by a green ball is 2/6, or one-third.

•Option B: Mary is more likely to draw a blue ball among the first two balls to be drawn, because 4/6 > 2/6

This option assumes that the probability of drawing a blue ball among the first two balls is 4/6, or two-thirds. However, there are three ways to get this outcome: BGR, BRG, and GBR. So, the probability of drawing a blue ball among the first two balls is 3/6, or one-half.

•Option C: Mary is more likely to draw a blue ball among the first two balls to be drawn, because 5/6 > 2/6

This option assumes that the probability of drawing a blue ball among the first two balls is 5/6. However, this is incorrect because there are only six possible outcomes, and only three of them have a blue ball among the first two balls. So, the probability of drawing a blue ball among the first two balls is 3/6, or one-half.

•Option D: Mary is more likely to draw a red ball followed by a green ball, because 5/6 > 2/6

This option assumes that the probability of drawing a red ball followed by a green ball is 5/6. However, as we saw in option A, the probability of this outcome is actually 2/6, or one-third.

Therefore, the correct answer is Option B: Mary is more likely to draw a blue ball among the first two balls to be drawn, because 3/6, or one-half, of the possible outcomes have a blue ball among the first two balls.