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Page 1
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The University of British Columbia
Sessional Exams – 2006 Term 2
Mathematics 318 Probability with Physical Applications, All sections
Dr. A.E. Holroyd, Dr. G. Slade
Last Name:
First Name:
Student Number:
Circle section number:
201 (Slade),
202 (Holroyd)
This exam consists of
8
questions worth
10
marks each. No aids are permitted.
Problem
total possible
score
1.
10
2.
10
3.
10
4.
10
5.
10
6.
10
7.
10
8.
10
total
80
1. Each candidate should be prepared to produce his library/AMS card upon request
.
2. Read and observe the following rules
:
No candidate shall be permitted to enter the examination room after the expiration of one half hour, or to leave
during the ﬁrst half hour of the examination.
Candidates are not permitted to ask questions of the invigilators, except in cases of supposed errors or ambiguities
in examination questions.
CAUTION  Candidates guilty of any of the following or similar practices shall be immediately dismissed from the
examination and shall be liable to disciplinary action.
(a) Making use of any books, papers or memoranda, other than those authorized by the examiners.
(b) Speaking or communicating with other candidates.
(c) Purposely exposing written papers to the view of other candidates.
The plea of accident or forgetfulness
shall not be received.
3. Smoking is not permitted during examinations
.
Page 2
April 18 2006
Math 318 Final Exam, all sections
Page 2 of 10
Tables on last page.
1. A closet contains 10 diﬀerent pairs of shoes (each pair consists of a left shoe and a right shoe,
so there are 20 shoes in total). 6 shoes are chosen at random. Find (do NOT simplify) the
probability that:
(a)
(3 points)
3 complete pairs are chosen;
(b)
(3 points)
exactly 1 complete pair is chosen;
(c)
(4 points)
at least one left shoe and at least one right shoe are chosen.
Page 3
April 18 2006
Math 318 Final Exam, all sections
Page 3 of 10
2. A certain coin lands on its edge with probability 1
/
1000 each time it is tossed. Carefully
explain your answers to the following. Give ACTUAL NUMERICAL ANSWERS, using (if
necessary) the approximations
π
≈
3
.
1; ln 2
≈
0
.
69;
e

1
≈
0
.
37.
(a)
(2 points)
What is the expected number of tosses until the ﬁrst time the coin lands on its edge?
(b)
(2 points)
How many times must the coin be tossed so that the expected number of times it lands
on its edge is 1?
(c)
(3 points)
How many times must the coin be tossed so that the probability it lands on its edge at
least once is approximately 1
/
2?
(d)
(3 points)
How many times must the coin be tossed so that the probability it lands on its edge at
least 1000 times is approximately 1
/
2?
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