Question

Question 3 Ice Cream Preferences 4 point(s) After working at an ice cream parlor for many years, the manager noticed some trends and decided to collect some data. The following are the results for the customers' ordering preferences: (1) 50% of the customers ordered Chocolate, 30% ordered Vanilla, and 20% ordered Strawberry (II) 80% of the customers ordered a Cone, while 20% ordered a Cup for their ice cream. (Il) The event "a randomly selected customer will order Chocolate" is independent from the event "a randomly selected customer will order a Cone (IV) The events "a randomly selected customer will order Strawberry" and "a randomly selected customer will order a Cup" are mutually exclusive (disjoint) Use the information above to fill out the table below. Be sure to provide explanations/show work for how you arrived at each answer Hint: Recall the definitions of independent events and mutually exclusive events on pages 40 and 41 of the lecture notes. Chocolate Vanilla Strawberry Cone Cup Total Total 0.80 0.20 0.50 0.30 0.20

Answer 1

As given the probability that a randomly selected individual selected cone is independent of individual selecting chocolate = p(cone and chocolate ) = p(cone) * p(chocolate) =0.80 * 0.50 = 0.40

So a) 0.40

B) 0.50 - 0.40 = 0.10

Similarly p(strawberry and cup) = p(strawberry) * p(cup) = 0.2 * 0.2= 0.04

So f) 0.04

E) 0.2 - 0.04 = 0.16

a + c + e = 0.80

0.40 + c + 0.16 = 0.80

C) = 0.80 - 0.56 = 0.24

D) 0.30-0.24 = 0.06

So, a= 0.40 , b= 0.10, c= 0.24, d=0.06, e= 0.16, f= 0.04