A contest contains two multiple choice questions. Question 1 has 4 possible answer choices with only one correct and question 2 has 5 possible choices with only one correct. Assume that questions one...

A contest contains two multiple choice questions. Question 1 has 4 possible answer choices with only one correct and question 2 has 5 possible choices with only one correct. Assume that questions one and two are independent of each other and that a correctly answered question receives a score of 1, else a zero (that means the best score for
an individual is a 2). To win a prize, two people must enter the contest and their total score will determine their winnings. Now, two friends, call them Pete and Susan, take the contest questions and answer them independently. Let X be the total number of points awarded to them.
(a) What is the probability mass function (pmf) of X?
(b) What is the expected value of X?
(c) What is the probability that X is no more than 2?