To determine the expected value each time you pull a marble you have to construct a table of probability distributions.
Given the event "pull one marble of a determined colour"
For each marble colour there is a corresponding probability of appearence. To calculate said probability you have to divide the number of marbles of that colour by the total number of marbles in the bag.
The bag contains:
1 red marble
2 blue marbles
47 green marbles
The total number of marbles is then: 1+2+47=50
And the corresponding probabilities:
Now for each red marble you pull you'll gain $10, for each blue marble you'll gain $5 and for each green marble you'll owe $3.
Let X represent the "amount of money earned at the end of the game"
Note: the first value is red because you loose 3 dollars for each green marble, "-$3"
With the probability distribution determined you can calculate the expected value (i.e. mean value) using the following formula:
You have to multiply each value of X by its corresponding probability and add them:
At the end of the game the expected earnings are -$2.42, this means that you'll owe your brother money.