how much (on the average) does the carnival gain on each play?

Question

A carnival game involves a box which contains one $10 coin, two $5 coins, and seven $1 coins. The player is allowed to remove one coin at random from the box and keep it. If it costs $3 to play this game, how much (on the average) does the carnival gain on each play?

Answer 1

Player win Probability Carnival gain

10 1/10 -7 (3-10)

5 2/10 -2 (3-5)

1 7/10 2 (3-1)

So expected gain for carnival = (-7) (1/10) + (-2) (2/10) + 2 (7/10) = [ -7 -4 + 14] / 10 = 3/10 = $ 0.30