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# Probability

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A bag has 4 red marbles, 5 white marbles, 6 blue marbles, and 7 green marbles. Three marbles are drawn from the bag (without replacement). What is the probability that they are all the same color?

Jul 9, 2022

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Probability is determined by the (number of successful outcomes)/(number of total outcomes)

The number of total outcomes is 22 * 21 * 20 as we are choosing 3 marbles without replacement.

We can split the number of successful outcomes into 4 cases.

1. All red marbles.

This is 4 x 3 x 2

2. All white marbles

5 x 4 x 3

3. All blue marbles

6 x 5 x 4

4. All green marbles

7 x 6 x 5

Adding all the cases up gievs us 414.

Therefore, the proability of choosing the same color is:$$\frac{414}{9240} = \frac{69}{1540}$$

Jul 9, 2022