Question

Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull out one marble, record its color, put it back in the box, and draw another marble. What is the probability of pulling out a red marble followed by a blue marble? Describe the process of finding the probability of finding a red marble followed by a blue marble. What effect did putting the first marble back in the box have on the problem? Describe the probability of finding a red marble followed by the blue marble. Explain why this is the case.

Answer 1

The probability of pulling out a red marble followed by a blue marble is 2/27.

Step-by-step explanation:

To find the probability of pulling out a red marble followed by a blue marble, we need to consider the individual probabilities of drawing a red marble and a blue marble.

First, calculate the probability of drawing a red marble on the first draw. There are 2 red marbles out of a total of 9 marbles, so the probability is 2/9.

Next, calculate the probability of drawing a blue marble on the second draw. Since the first marble is put back in the box, the number of blue marbles remains the same, which is 3 out of 9. So the probability is 3/9.

To find the probability of both events happening, multiply the probabilities together: (2/9) x (3/9) = 6/81, which simplifies to 2/27.

Therefore, the probability of pulling out a red marble followed by a blue marble is 2/27.