A Sporting Goods Store Announces a "Wheel of Savings" Sale

Essay

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! Show your work.
-What is the probability that the first gold winner (100%) is the fifth customer in line?