Question

Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. What is the probability of pulling out a red marble followed by a blue marble? The multiplication rule says to use P(red)×P(blue).

Describe the probability of finding a red marble.

Describe the probability of finding 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 from a box can be found using the multiplication rule. The probability of finding a red marble is 2/9 and the probability of finding a blue marble is 1/3. Putting the first marble back does not affect the probabilities.

Step-by-step explanation:

The probability of pulling out a red marble followed by a blue marble can be found using the multiplication rule.

To find the probability of finding a red marble, we divide the number of red marbles by the total number of marbles: P(red) = 2/9.

To find the probability of finding a blue marble, we divide the number of blue marbles by the total number of marbles: P(blue) = 3/9 = 1/3.

We can use the multiplication rule to find the probability of finding a red marble followed by a blue marble: P(red and blue) = P(red) × P(blue) = (2/9) × (1/3) = 2/27.

Putting the first marble back in the box before the second draw does not affect the probabilities because the marbles are being chosen independently each time.

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