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?
+288 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:\(\frac{414}{9240} = \frac{69}{1540}\)
