Question

The owner of a restaurant serving Continental-style entrees was interested in studying ordering patterns of patrons for the Friday-to-Sunday weekend time period. Records were maintained that indicated the demand for dessert during the same time period. The owner decided to study two other variables, along with whether a dessert was ordered, the gender of the individual and whether a beef entree was ordered. The results are as follows:

                                                  Gender

Dessert Ordered             Male                Female                Total

Yes                                   96                    40                      136

No                                   224              240                    464

Total                            320                  280                      600

                                                Beef Entree

Dessert Ordered             Yes                 No              Total

Yes                                     71                      65                         136

No                                   116                    348                         464

Total                                  187                    413                         600

A waiter approaches a table to take an order for dessert. What is the probability that the first customer at the table...

a. orders a dessert
b. orders a dessert or has ordered a beef entree?
c. is a female and does not order a dessert?
d. is a female or does not order a dessert?
e. Suppose the first person from the whom the waiter takes the dessert order is a female. What is the probability that she does not order dessert?
f. Are gender and ordering dessert independent?
g. Is ordering a beef entree independent of whether the person orders dessert?
h. Is there anything that you would do to increase the odds of a patron ordering dessert?

Answer 1

Answer)

a)

probability that first customer orders a dessert = no. of customers ordered dessert/ total customers

                                                                          = 136 / 600 = 0.227

b)

probability of orders a dessert or has ordered a beef entree = no. of order dessert/total customers + no. of beef entree/ total customer = 136/600 + (187/600 - 71/600) = 252/600 = 0.42

c)

probability of female customer not ordering desert = no. of females didn't ordered dessert / total customers

                                                                                 = 240/600 = 0.4

d)

probability of female customer or not ordering desert = no. of females / total customers + didn’t order dessert / total customers

                                                                                 = 280/600 + (464/600 - 240/600)

                                                                                  = 0.84

e)

Probability of no dessert given its a female customer   = [P(no dessert and female) | P(female)]

                                                                                      = 240/600 / 280/600

                                                                                       = 0.8527

f)

Probability of no desert = 464/600 = 0.7733

Probability of no dessert given its a female customer = 0.8527 P

which are not equal

thus, gender and ordering dessert are not independent,

g)

Probability of beef entrée and order dessert = 71/600 = 0.1183

Probability beef entrée and Probability of order dessert = (187/600) * (136/600) = 0.0706

which are not equal

thus ordering a beef entree is not independent of whether the person orders dessert