The daily special at a particular restaurant is a three-course meal consisting o

Question

The daily special at a particular restaurant is a three-course meal consisting of an entree, a starch, and a dessert. The choices of entree are: Chicken or roast beef; the choices of starch are: Pasta or rice or potatoes; and, the choices of desert are: Ice cream or Jello or apple pie or a peach. Consider the experiment consisting of the selection of a meal, that is, the selection of one entree, one starch, and one dessert. Hint: Use the inclusion–exclusion method to determine the number of outcomes in the unions. (a) How many outcomes are in the sample space? (b) Let A be the event that ice cream is chosen. How many outcomes are in A? (c) Let B be the event that chicken is chosen. How many outcomes are in B? (d) List all the outcomes in the event AB = A B. (e) Describe the event A B in words. How many outcomes are in A B? (f) Let C be the event that rice is chosen. How many outcomes are in C? (g) List all the outcomes in the event ABC = A B C. (h) Describe the event A B C in words. How many outcomes are in A B C?

Explanation / Answer

The choices of entree are: Chicken or roast beef ( 2 outcomes)

The choices of starch are: Pasta or rice or potatoes (3 outcomes)

The choices of desert are: Ice cream or Jello or apple pie or a peach (4 outcomes)

(a) How many outcomes are in the sample space?

Total outcomes are combination of entree , starch and dessert ie 2*3*4=24

(b) Let A be the event that ice cream is chosen. How many outcomes are in A?

2*3=6 (since ice cream is fixed, other things can vary in 6 ways)

(c) Let B be the event that chicken is chosen. How many outcomes are in B?

3*4=12

(d) List all the outcomes in the event AB = A B

3 outcomes

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