Reference no: EM131647555

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?