Question

Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow parmbles. you are going to pull out one marble, record its color, remove it from 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).

1. Describe the probability of finding a red marble.
2. describe the probability of finding a blue marble.
3. describe the process of finding the probability of finding a red marble followed by a blue marble if the first marble was permanently removed?
4. what effect did removing the first marble from the box have on the problem
5. describe the probability of finding a red marble followed by the blue marble if the first marble is removed?

Answer 1

Explanation:

Part A

The probability of finding a red marble. P(red) = red / total

Total = red + yellow + blue

Total = 2 + 4 + 3

Total = 9

P(red) = 2/9 = 0.22222

Part B

P(blue) = blue / total

P(blue) = 3/8 = 0.375

This means that the red marble is permanently gone. The total is different. It is eight not nine.

Part C

The probability of red followed by blue is just the answers to A and B multiplied.

P(red) followed by blue = 2/9 * 3/8

P(red) followed by blue = 0.22222 * 3.75

P(red) followed by blue = 0.0833333

If you are confident of your concellation abilities you could do this as

P(red followed by blue) = 2/9 * 3/8 = 1/3 *1/4 = 1/12 = 0.083333....

Part D

Removing the first marble had the affect of reducing the total number of marbles to 8 and the number of reds from 2 downto 1

Part E

The answer here is 1/12.