In the popular casino game `Red marbles rule', a player draws 4 marbles at random with replacement from an urn containing 96 green marbles and 4 red ones. The player receives a payoff based on the following table

# Red marbles Payoff $

0 $0

1 $1

2 $10

3 $100

4 $1000

A. What are the probabilities of receiving each of the different payoffs?

Describe how you found these probabilities. If you figured them out based on a known probability distribution, you can just name it and explain (briefly) why it is correct.

B. To playRed marbles rule,you pay $1, then draws your marbles and receive your payoff. If X = net profit from game, what is E(X)?