Question

In a keno game you choose 4 numbers from 30 and then 10 winning numbers are chosen. If you match all 4 you win $20, if you match 3 you win $15, if you match 2 you win $10 and if you match 1 or 0 you win nothing.   What would be the price of the ticket for this to be a fair game?

Answer 1

let X be gain from game

P(X=20)= P(match 4 number) =(10C4)*(20C0)/(30C4) =2/261

P(X=15) =P(match 3 number) =(10C3)*(20C1)/(30C4) =160/1827

P(X=10) =P(match 2 number) =(10C2)*(20C2)/(30C4) =190/609

therefore expected value of game =E(x)=xP(x) =20*2/261+15*160/1827+10*190/609 =$ 4.59

price of the ticket for this to be a fair game =$ 4.59