1. A house edge on slot machines in casinos varies tremendously, it is sometimes as high as 15%. This means that for every wager, the casino wins with probability 65% and loses with probability 35%. (Show you work) a. For a house edge of 15%, what is the expected value to the casino of $1 played in slot machines?

b. During a busy weekend at a casino, $5,000,000 is played in their slot machines. How much will the casino expect to make?

2. You are given 9 to 1 odds against tossing 3 tails in 3 tosses of a fair coin. This means you win $9 if you succeed and lose $1 if you fail. (Show you work) a. Find the expected value (to you) of the game. Round to the nearest cent.

b. How much money should you expect to win or lose in 100 games?

3. Consider a coin that lands on either heads or tails: a. If you flip the coin 10 times and the coin lands on heads 4 out of 10 times, should you suspect that the coin is unfair? Explain. (Show you work)

b. If you flip the coin 10,000 times and the coin lands on heads 4,000 out of 10,000 times, should you suspect that the coin is unfair? Explain.

4. An insurance policy sells for $1000. Based on past data, an average of 1 in 50 policyholders will file a $20,000 claim, an average of 1 in 200 policyholders will file a $30,000 claim, and an average of 1 in 400 policyholders will file a $60,000 claim. (Show you work) a. Find the expected value (to the company) per policy sold.

b. If the company sells 30,000 policies, calculate the expected profit or loss.