# Essay on Markov Chain and Probability

Submitted By ArunMannarsamy
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Pages: 15

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9780521740524c14.xml

CUAU021-EVANS

July 17, 2008

8:40

C H A P T E R

14

Revision

Revision of
Chapters 10–13
14.1

Multiple-choice questions

Questions marked with a † are based on Chapter 13.
1 Mary and Ann try to guess the month in which the other was born. The probability that both guess correctly is
A

1
2

B

1
6

1
4

C

D

1
24

E

1
144

2 Bag A contains 2 white and 3 black balls. Bag B contains 3 white and 2 black balls. If one ball is drawn from each bag the probability that they are of different colours is
6
10
13
21
24
A
B
C
D
E
25
25
25
25
25
3 Two dice are thrown. The probability of getting a sum that is greater than or equal to 12 is
1
1
1
1
B
C
D
E
A 0
6
12
18
36
4 A group consists of four boys and three girls. If two of them are chosen at random
(without replacement), the probability that a boy and a girl are chosen is
2
4
12
24
27
A
B
C
D
E
7
7
49
49
49
5 If X and Y are mutually exclusive events such that Pr(X) = Pr(Y ), then Pr(X ∪ Y) is
A Pr(X) × Pr(Y)

C Pr(Y)

B Pr(X)

E 1

D 0

6 In 1974, England won the toss in 250 of the 500 Tests played. The probability that
England wins the toss exactly 250 times in the next 500 Tests is
A 1
D

500
250

1
2

250

B

1
2

E

500
250

250

C
1
2

1
2

500

500

397
ISBN 978-1-107-67331-1
© Michael Evans et al. 2011
Photocopying is restricted under law and this material must not be transferred to another party.

Cambridge University Press

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P2: FXS

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Revision

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CUAU021-EVANS

July 17, 2008

8:40

Essential Mathematical Methods 1 & 2 CAS

7 If six fair dice are rolled, the probability of getting at least one 4 is
A

4
6

B

5
6

6

C 1−

5
6

6

D

1
6

E

1
3

8 If a card is randomly drawn from a well-shufﬂed bridge card deck (52 cards), the probability of getting a heart or a jack is
A

1
52

B

5
13

C

4
13

D

7
52

E

1
26

9 A bag contains k red marbles and 1 white marble. Two marbles are drawn without replacement. The probability that both are red is
A

k
(k + 1)2

B

k−1 k+1 C

k k+1 D

2k k+1 E

2 k+1 10 Two cards drawn at random from a pack. i The ﬁrst card is replaced and the pack shufﬂed before the second is drawn. ii There is no such replacement.
The ratio of the probabilities that both are aces is
A 8:3

B 5:3

C 4:3

D 17:13

E 52:51

11 The probability of Bill hitting the bullseye with a single shot is 12 . The probability that
Charles does the same is 14 . Bill has 2 shots and Charles has 4. The ratio of the probability of each player hitting the bullseye at least once is
A 64:27

B 2:1

C 32:27

D 192:175

E 64:85

12 The number of arrangements which can be made using all the letters of the word
RAPIDS, if the vowels are together, is
A 30

B 60

C 120

D 240

E 720

13 The number of ways in which n books can be chosen from m + n different books is
(m + n)!
C (m + n)! − n!
B (m + n)! − m!
A
n!
(m + n)!
(m + n)!
D
E m! m!n!
14 The number of different teams of seven which can be selected from a squad of
12 players is
E 396
D 120
C 5040
B 84
A 792
15 The number of four-letter code words which can be made using the letters P, Q, R, S if repetitions are allowed is
A 16

B 24

C 64

D 128

E 256

16 Six cards labelled 1, 2, 3, 4, 5 and 6 are put into a box. Three cards are then drawn from the box (without replacement). The probability that the three cards are all labelled with odd numbers is
1
1
1
1
1
E
D
C
B
A
20
12
8
4
2
ISBN 978-1-107-67331-1
© Michael Evans et al. 2011
Photocopying is restricted under law and this material must not be transferred to another party.

Cambridge University Press

P1: FXS/ABE

P2: FXS

9780521740524c14.xml

CUAU021-EVANS

July 17, 2008

8:40

Chapter 14 — Revision of Chapters 10–13

399

A 6 × 10 + 1 × 9
D 6 + 10 + 9
18 If Pr(A ∩ B) =

B 6 × 10 × 9
E 6 × 10 × 2

C 6 × 10 + 6 × 9

1
1
1 and Pr(B) = and Pr(B|A) = , then
5
2
3
2
1
and Pr(A) =
3
5
3
2
D Pr(A|B) = and Pr(A) =
3
5

1
3
and Pr(A) =
5
5
3
2
C Pr(A|B) = and Pr(A) =
5
5
2
2
E Pr(A|B) = and Pr(A) =