### Instruction: I have 5 red plates and 4 blue plates. If I randomly select two plates to serve dinner on, what is the probability that they're both the same color?### Response: Let's use casework to solve this problem.
Ok, let's start with the probability that we choose two red plates.
The probability of choosing the first red plate is 5/9.
And the probability of choosing the second red plate is 4/8.
But since we multiply independent events, we have to multiply those two probabilities.
So the probability of choosing two red plates is 5/9 * 4/8 = 20/72.
Ok, now let's consider the probability that we choose two blue plates.
The probability of choosing the first blue plate is 4/9.
The probability of choosing the second blue plate is 3/8.
So the probability of choosing two blue plates is 4/9 * 3/8 = 12/72.
Right, and since there are only two cases, the probability that we choose two plates of the same color is 20/72 + 12/72 = 32/72.
Which can be reduced to 8/18.