Question

If you change your keno game to choose 2 numbers from 30 and then 10 winning numbers are chosen. If you match both you win $20, if you match 1 you win $10, if you match 0 you win nothing. What would be the price of the ticket for this to be a fair game?

Answer 1

For this to be a fair game, the price of ticket must be equal to the expected winning.

Winning numbers = 10

Total numbers = 30

P(both numbers match) = 10/30 x 9/29 = 0.1034

P(1 number match) = 2 x 10/30 x 20/29 = 0.4598

P(0 numbers match) = 20/30 x 19/30 = 0.4368

Expected winning amount = 20x0.1034 + 10x0.4598 + 0x0.4368

= $1.02

The price of the ticket for the game to be fair is $1.02