Question: Disjoint or independent? In Exercise 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.
Exercise: M&M's. The Masterfoods company says that before the introduction of purple, yellow candies made up 20% of their plain M&M's, red another 20%, and orange, blue, and green each made up 10%. The rest were brown.
a) If you pick an M&M at random, what is the probability that
1) it is brown?
2) it is yellow or orange?
3) it is not green?
4) it is striped?
b) If you pick three M&M's in a row, what is the probability that
1) they are all brown?
2) the third one is the first one that's red?
3) none are yellow?
4) at least one is green?