1. The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 500 tickets. There is one $3,000 grand prize, four $400 second prizes, and eighteen $10 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

2.The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $5 each and will sell 900 tickets. There is one $2,000 grand prize, four $500 second prizes, and fifteen $10 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

3. A venture capitalist, willing to invest $1,000,000, has three investments to choose from. The first investment, a software company, has a 6% chance of returning $10,000,000 profit, a 41% chance of returning $3,500,000 profit, and a 53% chance of losing the million dollars. The second company, a hardware company, has a 7% chance of returning $8,000,000 profit, a 25% chance of returning $3,000,000 profit, and a 68% chance of losing the million dollars. The third company, a biotech firm, has a 12% chance of returning $6,000,000 profit, a 21% of no profit or loss, and a 67% chance of losing the million dollars. Order the expected values from smallest to largest. (Please if you can explain more because I see numbers and I am confused)

4. Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $6. If you roll a 2, 3, 4 or 5, you win $4. Otherwise, you pay $5. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate.

X	P(X)

b. Find the expected profit to the nearest cent. $

c. Interpret the expected value.

• If you play many games you will likely win on average very close to $2.83 per game.
• This is the most likely amount of money you will win.
• You will win this much if you play a game.

d. Based on the expected value, should you play this game?

• Yes, because you can win $6.00 which is greater than the $5.00 that you can lose.
• No, this is a gambling game and it is always a bad idea to gamble.
• No, since the expected value is negative, you would be very likely to come home with less money if you played many games.
• Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games.
• Yes, since the expected value is 0, you would be very likely to come very close to breaking even if you played many games, so you might as well have fun at no cost.

5. 26% of all college students major in STEM (Science, Technology, Engineering, and Math). If 35 college students are randomly selected, find the probability that a. Exactly 8 of them major in STEM.

b. At most 8 of them major in STEM.

c. At least 10 of them major in STEM.

d. Between 4 and 10 (including 4 and 10) of them major in STEM.

6. 65% of all violent felons in the prison system are repeat offenders. If 37 violent felons are randomly selected, find the probability that

a. Exactly 25 of them are repeat offenders.

b. At most 26 of them are repeat offenders.

c. At least 25 of them are repeat offenders.

d. Between 19 and 27 (including 19 and 27) of them are repeat offenders.