### Weary Of The Low Turnout In Student Elections A College Administration Decides T

Weary of the low turnout in student elections, a college administration decides to choose an SRS of three students to form an advisory board that represents student opinion. Suppose that 40% of all students oppose the use of student fees to fund student interest groups, and that the opinions of the three students on the board are independent. Then the probability is 0.4 that each opposes the funding of interest groups.(a)Call the three students A, B, and C. What is the probability that A and B support funding and C opposes it?(b)List all possible combinations of opinions that can be held by students A, B, and C. (Hint: There are eight possibilities.) Then give the probability of each of these outcomes. Note that they are not equally likely.(c)Let the random variable X be the number of student representatives who oppose the funding of interest groups. Give the probability distribution of X.(d)Express the event “a majority of the advisory board opposes funding” in terms of X and find its probability.