You draw and keep a single coin from a bowl that contains 14 ​pennies, 7 ​dimes, and 29 quarters. What is the expected value of the game to​ you?

Answer 1

Expected value is just a fancy way of saying mean value or mean return. To calculate it, we just multiply the monetary value of each coin by the chance that we draw it, and add together the results for each coin.

Our EV in pennies is 14/50 * 0.01 or .0028 dollars.

Our EV in dimes is 7/50 * 0.1 or .014 dollars.

Our EV in quarters is 29/50 * 0.25 or .145 dollars.

So we add these together and we expect to win .1618 dollars - just over 16 cents on average.