A couple wants to have 2 boys. They will continuous to have children until they have reached the goal. Assuming that the probability that they have 50% chance to have a boy or a girl. No twin or more are possible. Assuming that their goal is possible and has been fulfilled today!(Hints: 1. This is called "Negative Binomial Distribution. 2. Try to list all the possible outcomes.)

1. What is the probability that they have no girl?
2. What is the probability that they have exactly one girl?
3. What is the probability that they have exactly two girl?
4. What is the probability that they have in between 3 and 5 girls, inclusively?
5. What is the expected value of the number of children they have? (The mean)