Question

A bag contains 3 gold marbles, 26 silver marbles, and 28 black marbles. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you paid $1 to play this game?

Answer 1

3+26+28 = 57

chance of gold is 3/57

chance of silver = 26/57

chance of black = 28/57

the expected value of playing this game = a weighted average of the winnings (or losses) multiplied by the odds of winning: (3/57)3 + (26/57)2 + (28/57)(-1) = 9/57 + 54/57 - 58/57 = 60/57 -58/17 = 2/57 = about 0.578 winnings = $0.578 = 0.58 cents

You will win 0.58 cents each time you play this game, on average.

but the mode is on black. You're more likely to lose (28/57)(-1) about 0.49 cents on your first time to play

but if you stick it out, and play enough times, you'll average 0.58 cents a game