3) a computer store, 30% of the computers in stock are laptops and 70% are deskt

Question

3) a computer store, 30% of the computers in stock are laptops and 70% are desktops. Five percent of the laptops are on sale, while 10% of the desktops are on sale. a) Define the two events of interest and write, in proper notation, the four values given above. b) Use EITHER a tree diagram or a hypothetical two-way table to represent this situation. Calculate the probability of that a randomly selected computer will be a desktop, given that the computer is on sale. Use proper notation for it. c) d) Explain what that probability means. In an Italian breakfast café, a waitress has observed that 80% of her customers order coffee while the other 20% order a different drink. If a customer orders coffee, there is a 0.42 probability the customer will also order biscotti. On the other hand, only 15% of customers who ordered a different drink also order biscotti. Let B randomly selected customer orders biscotti and C # a randomly selected customer orders coffee. a) Create EITHER a hypothetical two-way table or a tree diagram to represent the situation. 4) a What is the conditional probability that a randomly selected customer ordered coffee, given that he/she ordered a biscotti? b) What is the conditional probability that a randomly selected customer did NOT order coffee, given that he/she ordered a biscotti? c)

Explanation / Answer

QUestion 2

Pr(Laptops) = 0.30

Pr(Desktops) = 0.70

Pr(Sale l laptops) = 0.05

Pr(sales l Desktops) = 0.10

(a)

(c) Pr( Computer will be desktop l Computer is on sale) = 0.07/0.085 = 0.8235

(d) That probability means that there is 0.8235 probability that if a computer is on sale than 0.8235 probability is there it will be desktop.

Question 4

Pr(Customers order coffee) = 0.80

Pr(Customers order different drink) = 0.20

Pr(Biscotti l Coffee) = 0.42

Pr(Biscotti l Coffee) = 0.15

(A) Two way table

(b) Pr(Customer ordered coffee given that she ordered a biscotti) = 0.336/0.366 =  0.918

(c) Pr(Custmor did not order coffee given that he ordered a biscotti) = 0.03/0.366 = 0.082

On sale Not on sale Total Type of Computer Laptops 0.015 0.285 0.3 Desktops 0.07 0.63 0.7 Total 0.085 0.915 1

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