You roll a single die: If you roll a 4 someone gives you $1, if you roll any other number you must give them 25 cents. What is your expectation if you play this game-in other words, how much money on average can you expect to win or lose everytime you roll the die when playing this game.
there is a 1/6 chance that you will win $1
there is a 5/6 chance that you will lose .25
you can expect to win (1/6)*1=.1666667
you can expect to lose (5/6*.25)=.2083333
.16667 - .20833 = -.04167
you can expect to lose an average of a bit more than 4 cents per roll of the dice