Let x be the probability of winning and let y be the probability of losing. Then we can write the following equation: 2x - y = -0.65 ..............(1) the sum of the probabilities of winning and losing must equal 1. x + y = 1............(2) Rearranging (2), gives: y = 1 - x ............(3) Plugging the expression for y from (3) into (1), we get: 2x - 1 + x = -0.65 which simplifies to: 3x = 0.35 Therefore x = 0.117 and y = 0.883. The expected value of the game will be a loss of 65 cents if the probability of winning is 0.117 and the probability of losing is 0.883.
