Question

A box contains five red, three blue, and two white poker chips. Two are selected without replacement. For example, BR is a possible outcome representing the first is blue and the second is a red. BR and RB are different outcomes.
a. list the sample space.
b. find the probability that both are the same color.

Answer 1

The sample space is the set of all possible outcomes of an experiment.
So, I believe the sample space is:
RR, RB, RW, BB, BR, BW, WW, WR, WB

There are 10-choose-2 = 45 possible draws of two chips. There 5-choose-2 =10 ways to choose 2 red chips. There are 3-choose-2 ways=3 to pick 2 blue chips, and 2-choose-2=1 ways to pick 2 white chips. Probability both chips are the same color is (10+3+1)/45 = 31.1%


The number of ways to draw