What is the probability of winning?

Question

Supposed a certain game is fair and costs 9$ if you lose and the net payoff of 4$ if you win. The only possible outcomes of the game are winning and losing. Is the answer 0.55?

Answer 1

If it's a "fair" game in the sense of expected winning = $0

then -9p + 4(1-p) = 0 where p=probability of losing and 1-p= probability of winning

-9p -4p =-4

-13p =-4

p =4/13 = about .31 = 31% chance of losing

1-p = 9/13 = about .69 = 69% chance of winning