I would greatly appreciate if someone could help me set up and solve the following two problems.
1. If 7 cards are dealt from an ordinary deck of 52 cards, what is the probability that exactly 2 of them will be face cards? That at least 1 of them will be a queen?
Using the hypergeometric distribution formula, I said that this would be equal to 12 choose 3 divided by 52 choose 7. What am I doing wrong?
2. A random committee of size 3 is selected from 4 doctors and 2 nurses. Write a formula for the probability distribution of the random variable X representing the number of doctors on the committee. Find P(2<=X<=3).