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.

a. Here is the sample space for the two chips being selected without replacement:

RR
RB
RW
BR
BB
BW
WR
WB
WW

b. To find the probability that both chips are the same color, we need to count the number of outcomes where both chips are red, blue, or white.

Total outcomes: 9 (from the sample space)
Outcomes where both chips are red: 1 (RR)
Outcomes where both chips are blue: 1 (BB)
Outcomes where both chips are white: 0

Therefore, there are 2 outcomes where both chips are the same color. So, the probability is 2/9 or approximately 0.22.

a. To list the sample space, we need to consider all the possible outcomes of selecting two chips without replacement. Let's denote "R" for red chips, "B" for blue chips, and "W" for white chips. The sample space is as follows:

RR, RB, RW, BR, BB, BW, WR, WB, WW

b. To find the probability that both chips are the same color, we need to count the number of favorable outcomes (both chips of the same color) and divide it by the total number of possible outcomes (sample space).

Favorable outcomes:
RR, BB, WW = 3 favorable outcomes

Total number of outcomes:
From the sample space above, we see that there are 9 possible outcomes, so the total number of outcomes is 9.

Therefore, the probability that both chips are the same color is 3/9 or 1/3.

To determine the sample space, we need to list all possible outcomes when picking two chips without replacement. Let's denote the different colors as R (red), B (blue), and W (white). We will use a combination of these letters to represent the outcomes.

a. The sample space is as follows:
RR, RB, RW, BR, BB, BW, WR, WB, WW

b. To find the probability that both chips are the same color, we need to calculate the number of outcomes where both chips are the same color and divide it by the total number of possible outcomes.

First, let's count the number of outcomes where both chips are the same color:
There are 5 red chips, so we can choose 2 red chips from 5 in C(5,2) or 5C2 ways.
There are 3 blue chips, so we can choose 2 blue chips from 3 in C(3,2) or 3C2 ways.
And there are 2 white chips, so we can choose 2 white chips from 2 in C(2,2) or 2C2 ways.

Therefore, the total number of outcomes where both chips are the same color is:
C(5,2) + C(3,2) + C(2,2) = 10 + 3 + 1 = 14

Now, let's calculate the total number of possible outcomes, which is the size of the sample space:
Since there are 10 chips in total, we can choose 2 chips from 10 in C(10,2) or 10C2 ways.

Therefore, the total number of possible outcomes is:
C(10,2) = 45

So, the probability that both chips are the same color is:
P(both same color) = Number of outcomes where both chips are the same color / Total number of possible outcomes
= 14 / 45

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