Please help with the following problem. I am trying tosolve the probability of e

Question

Please help with the following problem. I am trying tosolve the probability of each meal listed in this menu. It reads: Select one item from each category: main course: shrimp, pork chop, salmon andchicken, side items: grits, waffles, mashed potaotes and collardgreens drink item: coke, sprite, sweet tea and ginger ale dessert item: red velvet cake, sweet potatoe pie, banannapudding and peach cobbler. after conducting a survey of 45 people here are the resultsbased on the categories provided. Shrimp 11 Chicken 12 Pork Chop 4 Salmon 17 Grits 4 Waffles 8 Mashed Potatoe 22 Collard Greens 15 Sweet Tea 20 Coke 10 Ginger Ale 8 Sprite 9 Red Velvet Cake 12 Sweet Potatoe Pie 7 Banana Pudding 12 Peach Cobbler 16 I started this as: 4x4x4x4 = 256. There are 256 possible wayscustomers could order a meal; however, I was sure how to representthis info using the probability formula to find each mealprobability. Please help. Thanks. Please help with the following problem. I am trying tosolve the probability of each meal listed in this menu. It reads: Select one item from each category: main course: shrimp, pork chop, salmon andchicken, side items: grits, waffles, mashed potaotes and collardgreens drink item: coke, sprite, sweet tea and ginger ale dessert item: red velvet cake, sweet potatoe pie, banannapudding and peach cobbler. after conducting a survey of 45 people here are the resultsbased on the categories provided. Shrimp 11 Chicken 12 Pork Chop 4 Salmon 17 Grits 4 Waffles 8 Mashed Potatoe 22 Collard Greens 15 Sweet Tea 20 Coke 10 Ginger Ale 8 Sprite 9 Red Velvet Cake 12 Sweet Potatoe Pie 7 Banana Pudding 12 Peach Cobbler 16 I started this as: 4x4x4x4 = 256. There are 256 possible wayscustomers could order a meal; however, I was sure how to representthis info using the probability formula to find each mealprobability. Please help. Thanks. Shrimp 11 Chicken 12 Pork Chop 4 Salmon 17 Grits 4 Waffles 8 Mashed Potatoe 22 Collard Greens 15

Explanation / Answer

First, you need to find the probability of each of the four maincourses, side items, drink items, and desert items. This is simple going to be the number of occurances divided by 45for each, because each person orders exactly one of each ofthese. For example, the probability of getting shrimp is11/45. For each meal, you can find the probability by multiplying theprobability of the main course, side item, drink, and desert. Each of these has a denonimator of 45, and the numerator of thenumber of occurances. Thus, the probability of the meal = M * S * DR * DE / (45 ^ 4),where M is the occurances of the main, S is the occurances of theside, etc. For example, probability of Shrimp, Grits, Sweet Tea and Red VelvetCake is = 11 * 4 * 20 * 12 / (45^4)

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