### Instruction: The science club has 25 members: 10 boys and 15 girls.  A 5-person committee is chosen at random.  What is the probability that the committee has at least 1 boy and at least 1 girl?### Response: I need to find the probability of the event that the committee has at least 1 boy and at least 1 girl.
I can use the complement rule to find this probability, since it is easier to calculate the probability of the opposite event: that the committee has either no boys or no girls.
If the committee has no boys, then it must have 5 girls, and there are 15 choose 5 ways to do that.
If the committee has no girls, then it must have 5 boys, and there are 10 choose 5 ways to do that.
So the probability of the opposite event is (15 choose 5 + 10 choose 5) divided by the total number of ways to choose 5 people from 25, which is 25 choose 5.
I can use a calculator or the binomial coefficient formula to find these values.
15 choose 5 is 3003, 10 choose 5 is 252, and 25 choose 5 is 53130.
So the probability of the opposite event is (3003 + 252) / 53130, which is about 0.0612.
Therefore, the probability of the original event is 1 minus 0.0612, which is about 0.9388.