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?
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:\(\frac{414}{9240} = \frac{69}{1540}\)