Question

8. A sporting goods store announces a "Wheel of Savings" sale. Customers select the merchandise they want to purchase, then at the cash register they spin a wheel to determine the size of the discount they will receive. The wheel is divided into 12 regions, like a clock. Six of those regions are red, and award a 10% discount. The three white regions award a 20% discount and two blue regions a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100% discount - the merchandise is free! 10 2010 7100 40 10 20 10 40 a. What is the probability that a customer gets at least a 40% discount? b. What is the probability that three consecutive customers all get 20% discounts? c. What is the probability that none of the first four customers gets a discount over 20%? d. What is the probability that the first gold winner (100%) is the fifth customer in line?

Answer 1

Answer:

a) Probability that a customer gets at least a 40% discount is computed here as:

= Probability that he gets a region within 40% or 100%

= 3/12

= 0.25

Therefore 0.25 is the required probability here.

b) Probability that three consecutive customers gets 20% discount is computed here as:

= (Probability of 20% discount )3

= (3/12)3 = 0.015625

Therefore 0.015625 is the required probability here.

c) Probability that none of the first four customers gets a discount over 20% is computed here as:

= (Probability of > 20% discount )4

= (3/12)4

= 0.00390625

Therefore 0.00390625 is the required probability here.

d) Probability that the first gold customer is the fifth person in the line

= (Probability that first 4 ones are not gold ) * Probability that the fifth one is gold

= (11/12)4 * (1/12)

= 0.0588

Therefore 0.0588 is the required probability here.