16. [-/5 Points] DETAILS BBUNDERSTAT12 4.2.015. MY NOTES ASK YOUR TEACHER M&M plain candies come in various colors. According to the M&M/Mars Department of Consumer Affairs, the distribution of colors for plain M&M candies is as follows. Color Purple Yellow Red Orange Green Blue Brown Percentage 22% 23% 20% 5% 6% 3% 15% Suppose you have a large bag of plain M&M candies and you choose one candy at random. (a) Find P(green candy or blue candy). Are these outcomes mutually exclusive? Why? O Yes. Choosing a green and blue M&M is not possible. Yes. Choosing a green and blue M&M is possible. O No. Choosing a green and blue M&M is possible. O No. Choosing a green and blue M&M is not possible. (b) Find P(yellow candy or red candy). Are these outcomes mutually exclusive? Why? O No. Choosing a yellow and red M&M is not possible. O Yes. Choosing a yellow and red M&M is not possible. O Yes. Choosing a yellow and red M&M is possible. O No. Choosing a yellow and red M&M is possible. (c) Find P( not purple candy).Are customers more loyal in the East or in the West? The following table is based on information from a recent study. The columns represent length of customer loyalty (in years) at a primary supermarket. The rows represent regions of the United States. Less Than 1 Year 1-2 Years 3-4 Years 5-9 Years 10-14 Years 15 or More Years Row Total East 32 49 59 112 77 110 439 Midwest 31 67 68 120 63 153 502 South 53 70 93 158 106 197 677 West 41 74 67 78 45 85 390 Column Total 157 260 287 468 291 545 2008 What is the probability that a customer chosen at random has the following characteristics? (Enter your answers as fractions.) (a) has been loyal 10 to 14 years (b) has been loyal 10 to 14 years, given that he or she is from the East (c) has been loyal at least 10 years (d) has been loyal at least 10 years, given that he or she is from the West (e) is from the West, given that he or she has been loyal less than 1 year (f) is from the South, given that he or she has been loyal less than 1 year (g) has been loyal 1 or more years, given that he or she is from the East (h) has been loyal 1 or more years, given that he or she is from the West (i) Are the events from the East and loyal 15 or more years independent? Explain. O Yes. P(loyal 15 or more years) = P(loyal 15 or more years | East). O Yes. These events can occur together. O No. P(loyal 15 or more years) # P(loyal 15 or more years | East). O No. These events cannot occur together