7. Find the probability of a flopping a set in holdem given that you have a pocket pair (Express as % and round to 2 digits). 8. Draw a single card. Let A be the event that you get an ace and let B be the event that you get a spade. Are A and B independent events? Explain in terms of conditional probabilities. Your answer should verify an equation! 9. Find the probability of being dealt a blackjack from a six deck shoe. 10. Find the expected value in % of an insurance bet if you have removed 6 small cards from a single deck (and the dealer has an ace up). 11. You have 90JO and the turn board is QQTO5(24. Assume a straight or better is good. The pot is 100$ and villain bets $50. What is the expected value of a call? What are the pot odds? What would you do in this situation? 12. You have T.TO and the turn board is T4945424. You have flopped a set but the turn makes a flush likely. Assume the villain has A&. The pot is 90$ and villain bets $30. What is the expected value of a call? What are the pot odds? What would you do in this situation? 13. Suppose you are the house in European Roulette. A bet on a single number pays 35:1. What is the optimal bet as a percentage of the bankroll? 14. A dice game involving rolling 2 dice pays 6 units if you roll a total of 7, pays zero if you roll a 2 or 12, and you lose one unit otherwise. Find the expected value and standard deviation of a unit bet. 15. You bet 20 percent of your 100 dollar bankroll on a 60%-40% even money bet (using the Kelly optimal bet). Use the natural log utility function (corresponding to full Kelly) to find the expected value and variance of this bet. 16. Suppose you are on the river in a holdem game against a player that randomly bluffs half the time. You have the nuts and the player bets 100 dollars into a pot of 100 dollars. What is the expected value of a call? What if they only bluff one third of the time