A committee of 7 members is to be formed by selecting members at random from a pool of 14 candidates consisting of 5 women and 9 men.
a. What is the probability that there will be at least three women in the committee?
b. It is desired to increase the chance that there are at least three women in the committee to 80% by doing one of the following:
i. Adding more women to the pool.
ii. Removing some men from the pool. For each of the two options, find out how many should be added or removed.