Be sure this exam has 10 pages including the cover

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

.

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.

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?