Answer to Question #265387 in Statistics and Probability for ZINHLE

Question

The are 10 balls in a container, each one with a number printed on it from 1 to 10. Two balls are released from the container, one at a time, without replacement. You will win ten times the amount you paid to play the game if both balls which are released are even and less than 8. 

Determine the House Advantage

Answer 1

Let x be the amount of the fee paid to pay the game

avg net profit of house = $x*(1-\frac{10-8}{10C2}+(x-10x)*\frac{10-8}{10C2}=\frac{33x}{45}$

So, house $adv = \frac{avg \space net \space profit}{x} * 100 =\frac{\frac{33x}{45}}{x} * 100 = 73.33 \%$