Statistics task

Question

Suppose you have a box with 3 blue marbles, 2 red marbles, and 4 yellow marbles. You are going to pull one marble, record it’s 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 of the first marble was permanently removed?

4) What affect 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 is removed?

Answer 1

The probability P of a red is 2/9 because there are 2 red out of 9 total. The P(blue) is 3/8 because you remove one marble and did not replace it. Multiply 2/9 • 3/8 = 6/72 reduced to 1/12.

All these Probabilities are found the same, number colored ones divided by the total in the box. When you do not replace a marble the total, bottom number changes and the top can change if you draw the same color. The number of the color you want divide by the total in the box. Hope it helps

Answer 2

Note: The total number of marbles is 9

Given: 3 Blue, 2 Red, 4 Yellow

(1) P(red) = 2/9

(2) P(blue) = 3/9 = 1/3

(3) P(red, blue) without replacement = (2/9)*(3/8) = 1/12

(4) Removing the first red marble from the box

reduces the total number of marbles in the box

and increases the probability of picking a blue marble.

(5) I think this is the same question as #3 and 4.

For more fun, let's calculate some more probabilities...

P(blue, red) without replacement = (3/9)(2/8) = 1/12

P(blue, blue) without replacement = (3/9)(2/8) = 1/12

P(blue, blue, blue) w/o replacement = (3/9)(2/8)(1/7) = 1/84

P(blue, blue, yellow ) w/o replacement = (3/9)(2/8)(4/7) = 1/21

P(yellow, blue) w/o replacement = (4/9)(3/8) = 1/6

Answer 3

Total number of marbles = 3 blue + 2 red + 4 yellow = 9 marbles

1: P(red) = 2/9

2: P(blue) = 3/9 = 1/3

3: First find P(red) = 2/9

Once the red marble is found, it is removed from the rest of the marbles, leaving only 8 marbles.

Now find P(blue) = 3/8

Last find probability of picking red and then blue. P(red)P(blue) = 2/9 x 3/8 = 6/72 = 1/12

4: Removing the first marble Increases the probability of picking the next marble of a different color.

5: First find P(blue) = 1/3

Once the red marble is found, it is removed from the rest of the marbles, leaving only 8 marbles.

Now find P(red) = 2/8 = 1/4

Last find probability of picking blue and then red. P(blue)P(red) = 1/3 x 1/4 = 1/12

Answer 4