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Arizona State University
Math 119 Finite Mathematics Test 3 A
Graded test will be returned on 12/4/02.
Dr. S. Takahashi
Place your name label here:
Your Predicted Score: _____________
Your Actual Score:
_____________
Read the following before you take this test.
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Maximum total points for this test is 100.
You have 100 minutes to complete. Your score is reduced by one point per each minute exceeded.
Show all of your work. No work  No credit
No need to show work for true-or-false questions.
Make sure to define events wherever applicable.
Simplify solutions as far as possible. Do not leave solutions in symbolic forms, such as C 5,2 .
Use only Casio CFX-9850GB, TI-81, 83, 86 or ordinary non-graphing calculators, if needed.
Use scratch paper provided by the proctor and attach to the test.
Make sure you indicate your solutions by circling or boxing your final answers.
Before you start, make sure you have all 12 questions.
No rubber-necking.
Good luck.
Honor Statements:
(Standard ASU math dept. version)
By signing below you confirm that you have neither given nor received any unauthorized assistance on this
exam. This includes any use of a graphing calculator beyond those uses specifically authorized by the
Mathematics Department and your instructor. Furthermore, you agree not to discuss this exam with anyone
until the testing period is over. In addition, your calculator’s program memory and menus may be checked
at any time and cleared by any testing center proctor or Mathematics Department instructor.
Signature
Date
Mat 119 Test 3A: S. Takahashi
Page 2 of 5
Show all work, except for True or False questions. Throughout PE   probability of an event E .
1. True or False:
(2 points each)
ア） If two events are independent, then they must be mutually exclusive.
______________
イ） Ordered arrangements of distinct objects are called combinations.
______________
ウ） If E and F are two events in a sample space S , then PE F   PF E 
エ） The identity PE  
C E 
does not hold for equiprobable sample space S .
C S 
______________
______________
オ） If events E and F are independent, then PE F   PE   PF 
______________
2. Answer the following questions.
(4 points each)
①
Calculate the number of ways you can form a baseball team, consisting of 9 players, out of 17
athletes in class, provided which position each player plays is not an issue.
②
Calculate the number of ways you can form a baseball team, consisting of 9 players, out of 17
athletes in class, provided which position each player plays is an issue.
③
The Student Aptitude Committee has 6 faculty members, 2 administrative members, and 3
student members. Calculate the number of subcommittee of 3 faculty members, 1 administrator,
and 1 student that you can generate.
④
Calculate the number of different 7-letter words, real or unreal, that you can generate out of
English alphabet if repeated letters are not allowed
Copyright: S. Takahashi Arizona State University
Mat 119 Test 3A: S. Takahashi
Page 3 of 5
3. You are to toss a fair coin 6 times. Answer the following questions.
(3 points each)
ア) Calculate the number of possible distinct outcomes for this experiment.
イ) Calculate the number of distinct outcomes in which you get at most two tails.
ウ) Calculate the number of distinct outcomes in which you get at least one tail.
4. Consider a word “committee”. Answer the following two questions.
(5 points each)
イ） Calculate the number of distinct words, real or unreal, that can be generated from the word.
ロ） Calculate the number of distinct words, real or unreal, that can be generated from the word,
provided that the letter “i” precedes the letter “o”
5. Suppose you are conducting an experiment of tossing a fair coin and then rolling a fair die. (9 pts)
イ） Find the sample space for this experiment.
ロ） Find the event that the coin comes up heads.
ハ） Calculate the probability that the coin comes up heads.
Copyright: S. Takahashi Arizona State University
Mat 119 Test 3A: S. Takahashi
Page 4 of 5
6. Let E and F be two events in a sample space S . State, in a sentence or two, the difference between
PE  and P E F  . Can they be equal? Explain.
(5 points)
7. Parmema is taking two courses: comparative literature and differential geometry. His analysis, which is
quite accurate, tells that he has 0.6 probability of passing comparative literature course and 0.3
probability of passing differential geometry course. He is also certain that probability of passing at least
one of them is 0.8.
(10 points total)
ア） Calculate the probability of him passing both courses.
イ） He has decided to drop differential geometry if his probability of passing the course is less than
0.5. Should he drop differential geometry course, if he realizes that his probability of passing
both courses is now 0.2?
8. Calculate the probability that the 5-digit zip code contains the number “8”.
(5 points)
9. The box contains 59 tickets of distinct values, one of which is the winning ticket of $1,000,000. A
participant is to draw three tickets from the box. Calculate the probability that one of the three tickets
is the winning ticket.
(5 points)
Copyright: S. Takahashi Arizona State University
Mat 119 Test 3A: S. Takahashi
Page 5 of 5
10. In the swim meet, the odds for a senior swimmer to win are 1 to 2, and the odds for a sophomore
swimmer to win are 1 to 3. Calculate the probability and the odds that senior or sophomore wins the
meet, provided a tie is impossible.
(6 points)
11. In a supply container, there are 7 green pens, 8 black pens and 5 red ones. Two pens are taken
randomly in sequence without replacement. Calculate the probability that the first pen is green and the
second one is red.
(5 points)
12. The urn contains12 balls, 5 yellow, 4 white and 3 purple. Suppose you draw one ball from the urn, put
it back, and then draw another. Answer the following questions without using the tree diagram(s).
(10 points total)
ア) Calculate the probability that both balls are purple.
イ） Calculate the probability that one of the balls is purple.
Copyright: S. Takahashi Arizona State University