In a recent advertising campaign Applebees Restaurant offere

In a recent advertising campaign, Applebee\'s Restaurant offered diners a special 3-course menu for $15.99. The menu included choices of three appetizers (Mozzarella sticks, house salad, soup), four entrees (chicken, fish, beef, vegetarian pasta), and two desserts (ice cream, apple pie).
a. How many different 3-course meals can be ordered from this menu? (Draw a tree diagram to help visualize this sample space; or use the counting rule to find the total number of meals.)
b. How many of these 3-course meals have the beef course as the entrée?
c. How many of these 3-course meals do not have soup as the appetizer?
d. What is the probability that a 3-course meal has the chicken entrée?
e. What is the probability that a 3-course meal has either soup or salad?
f. What is the probability that a 3-course meal has either ice cream or apple pie for dessert?
g. What is the probability that a 3-course meal has shrimp cocktail as the appetizer?

Solution

We have :

3 appetizers. 4 entrees and 2 deserts to choose from.

So, ( we\'ll use the conting rule for each of the question)

a. How many different 3-course meals can be ordered from this menu?

= 3 ways * 4 ways * 2 ways = 24 ways
b. How many of these 3-course meals have the beef course as the entrée? (entre\'e fixed)

= 3 ways * 1 ways * 2 ways = 6 ways
c. How many of these 3-course meals do not have soup as the appetizer? ( 1 - lesser choice)

= 2 ways * 4 ways * 2 ways = 16 ways
d. What is the probability that a 3-course meal has the chicken entrée? (entree fixed)

= 3 ways * 1 ways * 2 ways = 6 ways

= 6/24

= 0.25
e. What is the probability that a 3-course meal has either soup or salad? (choice of only 2 appetizers)

= 2 ways * 4 ways * 2 ways = 16 ways

= 16 / 24

= 2/3
f. What is the probability that a 3-course meal has either ice cream or apple pie for dessert? (no choices lost)

= 3 ways * 4 ways * 2 ways = 24 ways

= 24 / 24

= 1
g. What is the probability that a 3-course meal has shrimp cocktail as the appetizer? (not an availabe option)

= 0 ways * 4 ways * 2 ways = 0 ways

= 0/24

= 0

Hope this helps.