# Thread: expected value of marbles

1. ## expected value of marbles

question:

We have 20 marbles in a bag, some red, some blue. We play the following game. We randomly pull a marble. If it is blue, we receive $10. Otherwise we pay$3. How many blue marbles are in the bag if we have an expected value of -$1.05 when playing this game? I'm not asking for the answer, just some guidance on how to get it. 2. Hello, graffitihead! We have 20 marbles in a bag, some red, some blue. We randomly drawl a marble. If it is blue, we receive$10. Otherwise we pay $3. How many blue marbles are in the bag if we have an expected value of -$1.05?

Let $\displaystyle B$ = number of blue marbles in the bag.
Then $\displaystyle 20 - B$ = number of red marbles in the bag.

We have: .$\displaystyle \begin{array}{c|c|c|} & \text{Prob.} & \text{Payoff} \\ \hline \hline \\[-4mm] \text{Blue} & \frac{B}{20} & +\$10 \\ \\[-4mm] \hline \\[-4mm]
\text{Red} & \frac{20-B}{20} & \text{-}\$3 \\ [-4mm] \\ \hline \end{array}$

The expected value is -$1.05 . .$\displaystyle \left(\tfrac{B}{20}\right)(+10) + \left(\tfrac{20-B}{20}\right)(\text{-}3) \;=\;\text{-}1.05 $And solve for$\displaystyle B\$ . . .