A fair coin is flipped four times

1. A fair coin is flipped four times.

(a) Write down the sample space.

(b) Find the probability that three heads are obtained.

(c) Find the probablility that the last two flips come up heads.

(d) Find the probability that exactly two heads are obtained.

2. A pizza place sells five sizes of pizzas, with 4 types of crust, 8 types of cheese, and 15 types of toppings. In how many ways can a 1-cheese, 1-topping pizza be ordered?

3. Find the following.

(a) 9! (d) 19P5

(b) 609!

605! (e) 19C5

(c) 9!− 2! (f) 4C1

4. A committee is to be formed containing five students, three professors and four administrators. If 20 students, 12 professors and 8 administrators are available, in how many ways can the committee be formed?

5. If there are fifteen runners in a race, in how many ways can first place, second place and third place be awarded?

6. An urn contains fifty purple marbles, ten green marbles, fifteen red marbles and twenty-five orangle marbles.

(a) If three marbles are chosen with replacement, what is the probability that all three are green?

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(b) If three marbles are chosen without replacement, what is the probability that all three are green?

(c) If one marble is chosen from the urn, what is the probability that is green or red?

7. Two cards are chosen without replacement from a standard deck. What is the probabiliy that both are jacks?

8. One card is chosen from a standard deck. What is the probability that it is a jack or is a ten?

9. One card is chosen from a standard deck. What is the probability that it is a jack or is red?

10. Suppose the odds in favor of a certain horse winning is race is 3:2. If you bet $100, and the horse wins, then you will win $300. What is the expected value of your bet?

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