Despite the repeated effort by the government to reform how Wall Street pays its executives, some of the nation’s biggest banks are continuing to pay out bonuses nearly as large as those in the best years before the crisis (The Washington Post, January 15, 2010). It is known that ten out of 15 members of the board of directors of a company were in favor of a bonus. Suppose three members were randomly selected by the media.
a. What is the probability that all of them were in favor of a bonus?
b. What is the probability that at least two members were in favor of a bonus?