There are five identical closed boxes One box contains 10000

There are five identical closed boxes. One box contains $10,000, two boxes contain $1000 each, one box contains $1, and the last box contains a miniature stop sign. A contestant is allowed to repeat this process until the box with the stop sign is opened; at this point, the game ends. Find the mean amount the contestant gets

How would you solve this using auxiliary variables?

Solution

1*10,000   +   2*1000    + 1*1    = 120001   /   5

mean amount = 2400.2