Question

Don will win $2 if he chooses Bag 1, $50 if he chooses Bag 2, and $100 if he chooses Bag 3. What is the expected value of the amount he will win?

Answer 1

Assuming that picking any bag is uniformly distributed (each bag has an equal chance of being picked), then if \(X\) is your winnings and \(f(x)\) is the pmf associated with your winnings, then your distribution can be represented like:


X | f(x)
2 | 1/3
50 | 1/3
100 | 1/3

Then the expected value is: \[ E(X)=\sum_{\text{all }x}xf(x)=2\left(\frac{1}{3}\right)+50\left(\frac{1}{3}\right)+100\left(\frac{1}{3}\right)\]