##### Document Text Contents

Page 6

IB Math – Standard Level – Probability Practice Alei - Desert Academy

C:\Users\Bob\Documents\Dropbox\Desert\SL\6StatProb\TestsQuizzesPractice\SLProbPractice1.docx on 02/09/2014 at 6:43 PM 6 of 7

13. Consider events A, B such that P (A) 0, P (A) 1, P (B) 0, and P (B) 1.

In each of the situations (a), (b), (c) below state whether A and B are

mutually exclusive (M);

independent (I);

neither (N).

(a) P(A|B) = P(A)

(b) P(A B) = 0

(c) P(A B) = P(A)

Working:

Answers:

(a) ..................................................................

(b) ..................................................................

(c) ..................................................................

(Total 6 marks)

14. In a school of 88 boys, 32 study economics (E), 28 study history (H) and 39 do not study either

subject. This information is represented in the following Venn diagram.

(a) Calculate the values a, b, c.

(4)

(b) A student is selected at random.

(i) Calculate the probability that he studies both economics and history.

(ii) Given that he studies economics, calculate the probability that he does not study history.

(3)

(c) A group of three students is selected at random from the school.

(i) Calculate the probability that none of these students studies economics.

(ii) Calculate the probability that at least one of these students studies economics.

(5)

(Total 12 marks)

a b c

39

H (28)E (32)

U (88)

Page 7

IB Math – Standard Level – Probability Practice Alei - Desert Academy

C:\Users\Bob\Documents\Dropbox\Desert\SL\6StatProb\TestsQuizzesPractice\SLProbPractice1.docx on 02/09/2014 at 6:43 PM 7 of 7

15. Let A and B be events such that P(A) = , P(B) = and P(A B) = .

(a) Calculate P(A B).

(b) Calculate P(AB).

(c) Are the events A and B independent? Give a reason for your answer.

Working:

Answers:

(a) …………………………………………..

(b) …………………………………………..

(c) ……………………………………..........

(Total 6 marks)

16. The following diagram shows a circle divided into three sectors A, B and C. The angles at the centre

of the circle are 90°, 120° and 150°. Sectors A and B are shaded as shown.

The arrow is spun. It cannot land on the lines between the sectors. Let A, B, C and S be the events

defined by

A: Arrow lands in sector A

B: Arrow lands in sector B

C: Arrow lands in sector C

S: Arrow lands in a shaded region.

Find

(a) P(B);

(b) P(S);

(c) P(AS).

Working:

Answers:

(a) …………………………………………..

(b) …………………………………………..

(c) …………………………………………..

(Total 6 marks)

2

1

4

3

8

7

A

B

C

150°

120°

90°

Page 13

IB Math – Standard Level – Probability Practice - MarkScheme Alei - Desert Academy

C:\Users\Bob\Documents\Dropbox\Desert\SL\6StatProb\TestsQuizzesPractice\SLProbPractice1.docx on 02/09/2014 at 6:43 PM 6 of 6

Required probability = (A1)(A1) 3

(c) (i) P(none in economics) = (M1)(A1)

= 0.253 (A1)

Notes: Award (M0)(A0)(A1)(ft) for = 0.258.

Award no marks for .

(ii) P(at least one) = 1 – 0.253 (M1)

= 0.747 (A1)

OR

3 (M1)

= 0.747 (A1) 5

[12]

15. (a) P(A B) = P(A) + P(B) – P(A B) (M1)

P(A B) =

= (A1)(C2)

(b) P(AB) = (M1)

= (A1) (C2)

(c) Yes, the events are independent (A1) (C1)

EITHER

P(AB) = P(A) (R1) (C1)

OR

P(A B) = P(A)P(B) (R1) (C1)

[6]

16. (a) (A1)(A1)(C2)

(b) (A2) (C2)

(c) (A1)(A1)(C2)

[6]

32

21

868788

545556

3

88

56

888888

545556

86

30

87

31

88

32

86

56

87

31

88

32

3

86

55

87

56

88

32

8

7

4

3

2

1

8

3

4

3

8

3

)P(

)P(

B

BA

2

1

120 1

0.333

360 3

90 120 210 7

0.583

360 360 12

90 3

0.429

210 7

1

4

7

12

Accept

IB Math – Standard Level – Probability Practice Alei - Desert Academy

C:\Users\Bob\Documents\Dropbox\Desert\SL\6StatProb\TestsQuizzesPractice\SLProbPractice1.docx on 02/09/2014 at 6:43 PM 6 of 7

13. Consider events A, B such that P (A) 0, P (A) 1, P (B) 0, and P (B) 1.

In each of the situations (a), (b), (c) below state whether A and B are

mutually exclusive (M);

independent (I);

neither (N).

(a) P(A|B) = P(A)

(b) P(A B) = 0

(c) P(A B) = P(A)

Working:

Answers:

(a) ..................................................................

(b) ..................................................................

(c) ..................................................................

(Total 6 marks)

14. In a school of 88 boys, 32 study economics (E), 28 study history (H) and 39 do not study either

subject. This information is represented in the following Venn diagram.

(a) Calculate the values a, b, c.

(4)

(b) A student is selected at random.

(i) Calculate the probability that he studies both economics and history.

(ii) Given that he studies economics, calculate the probability that he does not study history.

(3)

(c) A group of three students is selected at random from the school.

(i) Calculate the probability that none of these students studies economics.

(ii) Calculate the probability that at least one of these students studies economics.

(5)

(Total 12 marks)

a b c

39

H (28)E (32)

U (88)

Page 7

IB Math – Standard Level – Probability Practice Alei - Desert Academy

C:\Users\Bob\Documents\Dropbox\Desert\SL\6StatProb\TestsQuizzesPractice\SLProbPractice1.docx on 02/09/2014 at 6:43 PM 7 of 7

15. Let A and B be events such that P(A) = , P(B) = and P(A B) = .

(a) Calculate P(A B).

(b) Calculate P(AB).

(c) Are the events A and B independent? Give a reason for your answer.

Working:

Answers:

(a) …………………………………………..

(b) …………………………………………..

(c) ……………………………………..........

(Total 6 marks)

16. The following diagram shows a circle divided into three sectors A, B and C. The angles at the centre

of the circle are 90°, 120° and 150°. Sectors A and B are shaded as shown.

The arrow is spun. It cannot land on the lines between the sectors. Let A, B, C and S be the events

defined by

A: Arrow lands in sector A

B: Arrow lands in sector B

C: Arrow lands in sector C

S: Arrow lands in a shaded region.

Find

(a) P(B);

(b) P(S);

(c) P(AS).

Working:

Answers:

(a) …………………………………………..

(b) …………………………………………..

(c) …………………………………………..

(Total 6 marks)

2

1

4

3

8

7

A

B

C

150°

120°

90°

Page 13

IB Math – Standard Level – Probability Practice - MarkScheme Alei - Desert Academy

C:\Users\Bob\Documents\Dropbox\Desert\SL\6StatProb\TestsQuizzesPractice\SLProbPractice1.docx on 02/09/2014 at 6:43 PM 6 of 6

Required probability = (A1)(A1) 3

(c) (i) P(none in economics) = (M1)(A1)

= 0.253 (A1)

Notes: Award (M0)(A0)(A1)(ft) for = 0.258.

Award no marks for .

(ii) P(at least one) = 1 – 0.253 (M1)

= 0.747 (A1)

OR

3 (M1)

= 0.747 (A1) 5

[12]

15. (a) P(A B) = P(A) + P(B) – P(A B) (M1)

P(A B) =

= (A1)(C2)

(b) P(AB) = (M1)

= (A1) (C2)

(c) Yes, the events are independent (A1) (C1)

EITHER

P(AB) = P(A) (R1) (C1)

OR

P(A B) = P(A)P(B) (R1) (C1)

[6]

16. (a) (A1)(A1)(C2)

(b) (A2) (C2)

(c) (A1)(A1)(C2)

[6]

32

21

868788

545556

3

88

56

888888

545556

86

30

87

31

88

32

86

56

87

31

88

32

3

86

55

87

56

88

32

8

7

4

3

2

1

8

3

4

3

8

3

)P(

)P(

B

BA

2

1

120 1

0.333

360 3

90 120 210 7

0.583

360 360 12

90 3

0.429

210 7

1

4

7

12

Accept