In Exercise 39, you calculated probabilities of getting various M&M's. Some of your answers depended on the assumption that the outcomes described were disjoint; that is, they could not both happen at the same time. Other answers depended on the assumption that the events were independent; that is, the occurrence of one of them doesn't affect the probability of the other. Do you understand the difference between disjoint and independent?
a) If you draw one M&M, are the events of getting a red one and getting an orange one disjoint, independent, or neither?
b) If you draw two M&M's one after the other, are the events of getting a red on the first and a red on the second disjoint, independent, or neither?
c) Can disjoint events ever be independent? Explain.