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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

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CUAU021-EVANS

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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

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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) =