At a party, there are 10 people who like chocolate ice cream, 8 people who like vanilla ice cream, and 7 people who like strawberry ice cream. If two people are selected at random, what is the probability that both of them like the same flavor of ice cream?
Let's reason through this problem step-by-step:
1. There are a total of 25 people at the party (10 chocolate lovers + 8 vanilla lovers + 7 strawberry lovers).
2. We want to find the probability that two randomly selected people both like the same flavor of ice cream.
3. To do this, we can calculate the probabilities for each flavor separately and then add them together.
4. The probability that both people like chocolate is C(10, 2) / C(25, 2), which equals 45 / 300 ≈ 0.15.
5. The probability that both people like vanilla is C(8, 2) / C(25, 2), which equals 28 / 300 ≈ 0.093.
6. The probability that both people like strawberry is C(7, 2) / C(25, 2), which equals 21 / 300 ≈ 0.07.
7. Adding these probabilities together, we get 0.15 + 0.093 + 0.07 = 0.313.

The probability that both randomly selected people like the same flavor of ice cream is approximately 0.313.