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

(a) there are 24 out comes of sample space

n(S)=24

(b) n(A)=6

(c)n(B)=12

(d)n(AB)=3

(e) n(AUB)=n(A)+n(B)-n(AB)=6+12-3=15

(f)n(C)=8

(g) n(ABC)=1

(h)n(AUBUC)=n(A)+n(B)+n(C)-n(AUB)-n(AUC)-n(BUC)+n(ABC)=6+12+8-4-3-2+1=18

1 chicken pasta ice-cream 2 chicken pasta jello 3 chicken pasta apple pio 4 chicken pasta peach 5 chicken rice ice-cream 6 chicken rice jello 7 chicken rice apple pio 8 chicken rice peach 9 chicken potato ice-cream 10 chicken potato jello 11 chicken potato apple pio 12 chicken potato peach 13 roast beef pasta ice-cream 14 roast beef pasta jello 15 roast beef pasta apple pio 16 roast beef pasta peach 17 roast beef rice ice-cream 18 roast beef rice jello 19 roast beef rice apple pio 20 roast beef rice peach 21 roast beef potato ice-cream 22 roast beef potato jello 23 roast beef potato apple pio 24 roast beef potato peach

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