Question

You have a box with three blue marbles, two red marbles, and four 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? 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? Interpret the answer.

A. 1/7, 3/7, Multiplication rule, No effect, 3/49, Probability interpretation

B. 2/9, 4/9, Probability calculation process, Increased probability, 8/81,Probability interpretation

C. 1/5,2/5, Multiplication rule, Decreased probability, 2/25, Probability interpretation

D. 1/6, 1/3, Probability calculation process, No effect, 1/18, Probability interpretation

Answer 1

The probability of finding a red marble followed by a blue marble when drawing marbles from a box with three blue, two red, and four yellow marbles is 2/27.

Step-by-step explanation:

The probability of finding a red marble is 2/9, since there are two red marbles out of the 9 total marbles in the box. The probability of finding a blue marble is 3/9, since there are three blue marbles out of the 9 total marbles in the box.

To find the probability of finding a red marble followed by a blue marble, we multiply the probabilities: (2/9) x (3/9) = 6/81 = 2/27.

Putting the first marble back in the box means that the probabilities stay the same for the second draw. This is because the total number of marbles in the box remains the same, and the number of red and blue marbles also remains the same.

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