Maison Premiere is a famous bar in New York City. Based off past data, managemen

Question

Maison Premiere is a famous bar in New York City. Based off past data, management knows 61% of customers buy mixed drinks and 51% of their customers order appetizers. Analysis has shown that 40% of customers buy both a drink and an appetizer. 27% of customers also order dessert but seems to be independent of whether they order appetizers or drinks. (Organize the information before starting parts a through f) Let D = buys a drink, A = orders an appetizer, S = orders dessert. (Enter all answers rounded to 4 decimals)

a) Suppose a customer bought a drink. What is the probability the customer will order an appetizer?

b) If a customer ordered an appetizer, what is the probability that the customer will buy a drink?

c) Suppose a customer bought a drink. What is the probability that customer does not buy an appetizer?

d) Given a customer ordered dessert, what’s the probability they order an appetizer?

e) What’s the probability a customer orders a dessert and appetizer?

f) What’s the probability the customer buys a drink or an appetizer?

Explanation / Answer

a) P(A|D) =P(AnD)/P(D) =0.4/0.61=0.6557

b)P(D|A)=P(AnD)/P(A) =0.4/0.51=0.7843

c)P(Ac|D)=1-P(A|D) =1-0.6557 =0.3443

d)as they are independent it will remain 0.51

e)probability =0.51*0.27=0.1377

f) P(AUD) =P(A)+P(D)-P(AnD) =0.51+0.61-0.40=0.72

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