1, M%Ms [8 points] Around 2008, the Mars company stated that the distribution of colors in a bag of plain M&Ms was 13% brown, 16% green, 20% orange, 13% red, 14% yellow, and the rest were blue. (a) If you pick an M&M at random, what is the probability that 1. it is blue? 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? Problem 2, Disjoint or Independent? [3 points] In Problem 1, 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. Problem 3, Shirts [4 points] The soccer team's shirts have arrived in a big box, and people just start grabbing them, looking for the right size. The box contains 4 medium, 9 large, and 8 extra-large shirts. You want a medium for you and one for your sister. Find the probability of each event described. (a) The first two you grab are the wrong sizes. (b) The first medium shirt you find is the third one you check. (c) The first four shirts you pick are all extra-large. (d) At least one of the first four shirts you check is a medium