MATH 182
Roberson
Spring 2010
Exam 2
No notes, books, or other materials allowed. Calculators are acceptable (no sharing).
Please turn off cell phones and put away all other electronic devices besides your calculator.
Be sure to read all the directions carefully.
SHOW ALL WORK
For grading purposes:
Problem Number
Score
1
2
3
4
5
6
7
8
9
10
Bonus
Total
Total
15
9
6
15
10
8
14
10
8
5
5
105
(out of 100pts)
Name:______________________________________
1
MATH 182
Roberson
Spring 2010
1. A box has 2 red chips, 5 green chips, and 4 blue chips. Suppose the experiment is randomly selecting
one chip from these eleven.
a) Describe the sample space in terms of color. (3 points)
b) Find the probability of each outcome in the sample space. (3 points)
c) What type of probability did you use to answer part b? (3 points)
d) Could you use experimental probability to determine the probabilities you found in part b? If so,
how? If not, why not? (3 points)
e) If I repeat this experiment 500 times, how many times would I expect to draw a green chip?
(3 points)
2. Suppose that you are rolling a normal die (this is the singular of “dice”).
a) If you roll it 360 times, how many 4’s would you expect? (3 points)
b) If you roll the die 12 times and do not get any 4’s, does this mean that the die is not fair?
(3 points)
c) If you roll the die 360 times and do not get any 4’s, does this mean that the die is not fair?
(3 points)
2
MATH 182
Roberson
Spring 2010
3.
a) What is the largest possible value for a theoretical probability? (1 point)
b) Why is this the largest possible value for a theoretical probability? Include an example in your
explanation. (5 points)
4. Be sure to use correct notation when conveying your answers.
Suppose that I have seven cards in my hand: 3♥, Q♥, 5♦, K♦, 4♠, J♠, Q♠
If I draw a card at random:
a) What is the probability that it is a heart? (3 points)
b) What is the probability that it is a face card? (3 points)
c) If I repeat this experiment 84 times, how many times would I expect to get a face card?
(3 points)
d) If all I care about is what suit the card is, what does the sample space look like? (3 points)
e) What is the probability associated with each suit? (3 points)
3
MATH 182
Roberson
Spring 2010
5. Jackson is trying to convince his brothers, Jared and Kyle, to play a game. “It’s simple,” says Jackson,
“We’ll flip two coins. If they are both heads, then Jared gets a point. If they are both tails, them Kyle
gets a point. If one is a head and one is a tail, then I get a point.” Jackson says this is a fair game
because it covers everything in the sample space ( { HH, TT, HT} ).
Is this a fair game? Why or why not? (10 points)
6. Draw a rug that satisfies the following: (8 points)
1
P(white) = 3
1
P(gray) = 4
5
P(black) = 12
4
MATH 182
Roberson
Spring 2010
7. Suppose we have a bag with 2 red balls, 3 blue balls, and 4 green balls and we are going to draw two
balls without replacement.
a) Draw a tree diagram to model this situation and include all possible outcomes and their
associated probabilities. (8 points)
b) What is the probability that both balls are red? (2 points)
c) What is the probability that at least one of the balls is blue? (2 points)
d) What is the probability that the second ball is green given that the first ball is blue? (2 points)
5
MATH 182
Roberson
Spring 2010
8. Determine whether the following events are independent and/or mutually exclusive. Explain your
choice. (10 points)
Suppose two words are to be randomly selected from the following list: work, study, book,
bread, water. If words are not replaced, are the events “selecting the word book” and “selecting
the word bread” independent? Are they mutually exclusive?
9.
a) Suppose a class of twenty-eight students is having a 100 meter dash in which first place, second
place, and third place will be determined. Explain how you could determine the number of ways
the first three finishers turn out. (5 points)
b) How many ways can the first three finishers complete the race? (3 points)
6
MATH 182
Roberson
Spring 2010
10. Explain the importance order plays in the differences between finding the number of permutations and
finding the number of combinations. (5 points)
Bonus (5 points)
Relate the differences you described in question 10 to the formulas for finding the number of
𝑛!
combinations (n𝐶𝑟 = 𝑟! 𝑛 −𝑟 !) and for finding the number of permutations (n𝑃𝑟 =
𝑛!
).
𝑛 −𝑟 !
7