7.1-7.6, 8.1-8.4
Circle the correct classification of the following random variables. Find the values
the random variable may have. (4 pts each)
1. Z = the distance a vacationer travels.
finite discrete
infinite discrete
continuous
Values of X: x  0
2. U = the number of hours a day a woman works.
finite discrete
infinite discrete
continuous
Values of X: 0  x  24
3. Y = the number of tails that occur when a coin is tossed 6 times.
finite discrete
infinite discrete
continuous
Values of X: 0, 1, 2, 3, 4, 5, 6
4. X = the number of students draws without replacement to get a blue marble from a box
containing 4 red and 5 blue marbles.
finite discrete
infinite discrete
continuous
Values of X: 1, 2, 3, 4, 5
The random variable X may only assume the values 2, 3, 4, 5, and 6. Carefully
examine the given histogram, and find the following. If necessary, round answers to
3 decimal places. (2 pts each)
9. P(X = 5) = .2
10. P(X >3) = .4
11. Mode of X = 3
0.7
0.6
0.5
12. Median X = 3
13. Var(X) = 1.64
0.4
0.3
0.2
0.1
0 1 2 3 4 5 6 7 8 9
14. Write the non-uniform sample space formed when picking a letter at random from the
word MATHEMATICS. (4 pts)
{M, A, T, H, E, I, C, S}
15. E and F are mutually exclusive events and P(E) = 0.65 and P(F) = 0.2.
Find P(F  EC). (4 pts)
.35
16. The uniform sample space for an experiment is S = {1, 2, 3, 4, 5}. How many events
contain an odd integer? (4 pts)
32 – n(no odd integer) = 32-4 = 28
17. If the probability that Cara passes her math test is
5
, what are the odds that she fails
8
her math test? (4 pts)
3/5
An experiment consists of rolling a fair six-sided die (numbered 1-6) and a fair fivesided die (numbered 1-5). Answer the following four questions about the
experiment. (3 pts each)
18. How many events are associated with this experiment?
230 or 1,073,741,824
19. Let E be the event that the six-sided die shows an odd number and let F be the event
that the sum of the dice is either 4 or 5. Find P(E F).
P(E  F) = P(E) + P(F) – P(E  F) = 15/30 + 7/30 – 4/30 = 18/30 = 3/5 or .6
20. For the events in problem #19, find P(E | F).
P(E | F) = P(E  F)/P(F) = (4/30)/(7/30) = 4/7
21. Are the events in problem #19 independent events? Why or why not?
No, because P(E  F)  P(E) P(F)
P(E  F) = 2/15
and P(E) P(F) = (1/2)(7/30) = 7/60
The letters of the word SUPERCALIFRAGILISTIC are placed on slips of paper and placed
into a box. You randomly select 6 pieces of paper from the bag.
22. What is the probability that you select all of the I’s? (4 pts)
[C(4,4) C(16,2)]/C(20,6) = 1/323
23. What is the probability that you select at least 5 consonants? (4 pts)
[C(12,5)C(8,1) + C(12.6)]/C(20,6) = 121/646
Given the following tree diagram and that G is the event that a student is enrolled in
a math class and H is the event that a student is enrolled in a chemistry class,
answer the following four questions. (3 pts each)
H
0.65
G
0.35
HC
0.4
H
0.6
0.55
GC
0.45
HC
24. What is the probability that a randomly selected student is enrolled in a math class
and a chemistry class?
.4(.65) = .26
25. What is the probability that a randomly selected math student is enrolled in a
chemistry class?
.65
26. What is the probability that a randomly selected student is enrolled in a math class?
.4
27. What is the probability that a randomly selected chemistry student is not enrolled in a
math class?
.33/(.26 + .33) = 33/59
28. Draw a tree diagram to represent the following problem. Clearly define your events
and indicate the appropriate probabilities on each branch. (12 pts)
At the county fair you pay $3.00 to play in the following game.
A spinner device is numbered from 1 to 3, and each of the numbers is as likely to
come up as any other. You bet $1 on a given number. If the pointer comes to rest
on your chosen number, you win $4 (and get the bet back); otherwise, you lose the
$1 bet.
29. Find the probability distribution of your net winnings. (6 pts)
X
P(X)
1
1/3
-4
2/3
30. What are your expected net winnings? (4 pts)
E(X) = 1(1/3) – 4(2/3) = 1/3 – 8/3 = -7/3  -2.33, a loss of $2.33
31. If the winnings stay the same, what should be the price for the game to make it a fair
game? (4 pts)
1/3(4 – P) + (2/3)(-1 – P) = 0
P = 2/3
The price should be 67 cents to make the game fair.