According to officials of Mars, the makers of M&M Plain Chocolate Candies, 20% of the candies in each bag are red. Four candies are selected from a bag and the number of red candies is recorded.

a) Determine a probability distribution for this scenario. (Define the experiment, determine the possible values of the distribution and compute the probabilities. Show your work in the calculations. Do not use Excel or lookup tables.)

b) Suppose that instead of four, a sample of 22 candies is selected at random from a (large) bag. Find the expected number of non-red candies.

c) Find the probability that in a sample of 10 candies, at least 9 are not red.

d) Find the probability that in a sample of 10 candies at most 1 is red.

e) Compare parts (c) and (d). Explain/describe your findings.