a sporting goods store announces a \"Wheel of Savings\" sale. customers select t
ID: 3262550 • Letter: A
Question
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 a award a 10% discount. 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 i00% discount -the merchandise is free! Show your work 20 10 10 40 10 100 10 20 20 10 10 40 27) What is the probability that a customer gets at least a 40% discount? 28) what is the probability that two customers in a row get only 10% discounts? 29) what is the probability that three consecutive customers all get 20% discounts? 30) what is the probability that none of the first four customers gets a discount over 20%? 31) What is the probability that the first gold winner (100%) is the fifth customer in line? 32) What is the probability that there is at least one gold winner among the first six customers?Explanation / Answer
27) P(at least 40) = P(40 U 100) = P(40) + P(100) = 2/12 + 1/12 = 3/12 = 0.25
28) P(1010) = P(10)P(10) = 6/12 6/12 = 36/144 = 0.25
29) P(202020) = P(20) P(20) P(20) = (3/12)^3 = 0.016
30) P(not over 20) = 1 – P(over 20) = 1 – P(at least 40) = 1 – 0.25 = 0.75.
Then P(4 in a row not over 20) = (0.75)^4 = 0.316
31) P(not gold) = 1 – P(gold) = 1 – 1/12 = 11/12.
Then P(4 not gold, then gold) = (11/12)^4 (1/12) = 0.059
32) P(at least one gold) = 1 – P(no gold in six) = 1 – (11/12)^6 = 1 – 0.593 = 0.407
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