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 = number of blue marbles in the bag.
Then = number of red marbles in the bag.
We have: .
The expected value is -$1.05
And solve for . . .