3. At a casino, you are playing a game of chance against a professional gambler where you roll a pair of 8-sided dice. If the dice have a sum of 4 or 5, you gain $140, otherwise you lose $23.

a) Give the probability distribution for this game. Explain what each entry in your table means.

b) Find the expected value of this game. What would this mean if you played 7900 games?

c) Should you play this game? Why or why not?

d) How could you modify this game to be relatively fair to both players? Show the details.

4. Consider the following two situations.

a) Surgeries in a clinic occur randomly at an average of 2.9 surgeries per hour. What is the probability of observing at least three surgeries in a given hour at the clinic?

b) IBM produces transistors with a 12% defect rate. In a batch of 500 transistors, what is the probability that none are defective?