
x: 
$100 
$50 
$10 
$0 
p(x): 
.1 
.2. 
.3 
? 
11. Pepsi had an iTunes promotion in which one in three bottles won a free song. If John bought a bottle of Pepsi from a machine three mornings in a row,
12. Are these probability distributions? Explain why or why not.
13. P(X) = x/15 for x = 1, 2, 3, 4, 5 is a probability distribution.
14.Show that the following is or is not a valid
probability distribution:
For x = 0, 1, 2, 3: P(x) = x!/10
(x! is x factorial.)
15. For x = 2, 3, 4, let P(x) = (x*(x+1))/38.
Is this a probability distribution? Why or why not? If it is
a probability distribution, calculate its mean.
16. Suppose a bill can be selected from one of three hats. In the first hat there are five onedollar bills and five tendollar bills. In the second hat there are three fives and one ten, and in the third there are four tens.
17. John has constructed a wheel like the wheel on "Wheel of Fortune." It has twenty slots on which the arrow can land, and the arrow is equally likely to land on any one of the twenty slots. He paints fifteen of the slots white, four green and one red. He wants to use this wheel as a gambling game to raise money for charity, and decides that he will pay nothing if it lands on the white, one dollar if it lands on green, and $20 if it lands on the red slot.
















18. Suppose that you have a regular tetrahedron (a polyhedron with four surfaces) and a cube. The surfaces of the tetrahedron are numbered one through four, the cube one through six. These polyhedrons are tossed together, and the combinations that are on the bottom are recorded.
19. Suppose that you have a regular tetrahedron (a polyhedron with four surfaces) and a cube. The surfaces of the tetrahedron are numbered one through four, the cube one through six. These polyhedrons are tossed together, and the combinations that are on the bottom are recorded.
20. What is the probability that four cars drawn at random from a deck of cards will all be red? (Assume that they are not replaced.)
21. Consider the following rule for assigning probabilities:
Event: 
3 
4 
5 
Probability: 
2/3 
1/6 
1/6 
a) Does this rule fulfill the requirements to be a probability distribution? Explain why or why not.
b) What is the probability that either a 4 or a 6 will occur if we take one observation from this distribution?
c) If we took a very large sample from this distribution, say 1000 observations, and found the sample mean, what number should this sample mean be very close to?
22. Suppose you take a die and alter it, changing the five into a two. The sample space now has these possibilities: 1, 2, 3, 4, 6. What are the probabilities that should be attached to each? What is the expected value or mean of this probability distribution?
For some binomial distribution questions, go here.)