25% of u tomers buyo son Premiere is a amous bar in New York City. ase off past

Question

25% of u tomers buyo son Premiere is a amous bar in New York City. ase off past data, management kno s 55 % o customers buy mixed drinks and55 of their customers or er appetizers Ana appetizer. 16% of customers also order dessert but seems to be independent of whether they order appetizers or drinks. Organize the inform ation before starting parts a rough s as sho wn ha ad and an 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 wil order an appetizer? b) If a customer ordered an appetizer, what is the probability that the customer will buy a drink? cSuppose a customerbought a drink. What sobabilty that customer does not buy an izer? 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(A and D)/P(D)=0.25/0.55=0.4545

b)P(D|A)=0.25/0.55=0.4545

c)P(Ac|D)= 1-P(A|D)=1-0.4545=0.5455

d)P(A|S)=P(A)=0.55

e)P(S and A)=0.16*0.55=0.0880

f)P(D or A)=P(D)+P(A)-P(D and A)=0.55+0.55-0.25=0.85

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