# What is the probability that a customer gets at least a 40% discount?

1. Jan 30, 2005

### mutzy188

I'm really not good at probability and I would appreciate it if someone could check to see if I'm doing this right. Thanks

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 the wheel to determine the size of the discount they will receive. The wheel id 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 award a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100% discount-the merchandise is free!

1. What is the probability that a customer gets at least a 40% discount?
Work:
(3/12) = 25%

2. What is the probability that 2 customers in a row get only 10% discounts?
Work:
(6/12)(6/12) = 25%

3. What is the probability that 3 consecutive customers all get 20% discounts?
Work:
(3/12)(3/12)(3/12)= 1.6%

4. What is the probability that none of the first 4 customers gets a discount over 20%?
Work:
(9/12)(9/12)(9/12)(9/12) = 31.6%

5. What is the probability that the first gold winner (100%) is the fifth customer in line?
Work:
(11/12)(11/12)(11/12)(11/12)(1/12)= 5.89%
6. What is the probability that there is at least one gold winner among the first six customer?
Work:
1-[(11/12)(11/12)(11/12)(11/12)(11/12)(11/12)] = 40.6%

Is this correct? Thanks

2. Jan 30, 2005

### christinono

Looks perfect to me.

3. Jan 30, 2005

### mutzy188

for number 1 does the "at least" mean anything??

4. Jan 30, 2005

### christinono

It means anything equal to or more than 40%. In this case, it would be 40% or 100% (total of 3 possibilities).

5. Jan 30, 2005

ok thanks