
Probability
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 gamein 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