1. Suppose a jar contains 19 red marbles and 35 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red. Write the answer as a reduced fraction.

2. Tom buys a bag of cookies that contains 5 chocolate chip cookies, 9 peanut butter cookies, 9 sugar cookies and 4 oatmeal cookies. What is the probability that Tom reaches in the bag and randomly selects a sugar cookie from the bag, eats it, then reaches back in the bag and randomly selects a chocolate chip cookie? Write your answer as a percent. Round to the nearest tenth of a percent.

3. A jar contains 8 red marbles numbered 1 to 8 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability of the given event. Write your answers as reduced fractions.

a. the marble is red

b. the marble is odd-numbered

c. the marble is red or odd-numbered

d. the marble is blue and even-numbered

4. 3 letters are typed, without repetition. What is the probability that all 3 will be vowels? Write the answer as a percent. Round answer to three decimal places.

5. In a certain state's lottery, 45 balls numbered 1 through 45 are placed in a machine and seven of them are drawn at random. If the seven numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order in which the numbers are drawn does not matter.

a. Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket. Write the answer as a reduced fraction.

b. A single lottery ticket costs $2. Compute the Expected Value, to the state, if 10,000 lottery tickets are sold. Round the answer to the nearest dollar. c. A single lottery ticket costs $2. Compute the Expected Value, to you, if you purchase 10,000 lottery tickets. Round the answer to the nearest dollar.