1.	(a)	(i)	0.23	(A1)	(C1)
(ii)	0.21 + 0.15 = 0.36	(A1)	(C1)
Note: Accept equivalent answers
 
(b)	1200 × 0.23	(M1)
= 276	(A1)	(C2)
Note: Follow through from candidate’s answer in part (a)(i)
[4]

2.	(a)	 or 6 % or 0.06	(A1)	(C1)
 
(b)	 or  or 90 % or 0.9	(A1)	(C1)
 
(c)	 or  or 0.889 (3 s.f.)	(A2)	(C2)
Note: Award (A1) for 16 and (A1) for 18
[4]

3.	(a)	(i)	p(green) = 	(A1)
(ii)	p(not green) = 	(A1)
Note: Accept , 0.5 or 50 % for either answer
 
(b)	(i)	p(G½G) =  or 0.444 (3 s.f.)	(A1)
(ii)	p(not green then not green)
= 	(M1)
=  or  or 0.222 (3 s.f.)	(A1)

(iii)	p(one green and one not green)
= 	(M2)
Note: Award (M1) for , (M1) for (×2)
	=  or  or 0.556 (3 s.f.)	(A1)
 
(c)	(i)	p(3 green) = 	(M1)
	 =  or  or 0.0833 (3 s.f.)	(A1)
 
(ii)	p(only one green) = 3 × 	(M2)
Note: Award (M1) for , (M1) for (×3)
	=  or 0.417 (3 s.f.) or  or 	(A1)
 
(iii)	p(at least one green) = 1 – p(no green)
= 1 – 	(M1)
= 1 – 
=  or  or 0.917 (3 s.f.)	(A1)
[15]

4.	(a)	0.75 × 0.82	(M1)
= 0.615 	(A1)
 
(b)	0.25 × 0.18	(M1)
= 0.045 	(A1)
[4]

5.	(a)	(i)
		(A3)	3
Note: Award (A1) for a correct diagram (labelled), (A1) for x in the correct position, (A1) for either (48 – x) or (44 – x) correctly positioned.
 
(ii)	48 – x + x + 44 – x = 60 (or equivalent), allow ft from (i)	(M1)
Þ x = 32	(A1)	2
 
(iii)	The set of members who did not attend for both	(A2)	2
Drama and Sports (or equivalent)
 
(iv)	P(D or S) = 	(M1)(M1)
Note: Award (M1) for either  or , (M1) for adding.
	=  or  or 0.467 (3 s.f.) or 46.7 % (3 s.f.)	(A1)	3
 
(b)	(i)	P(Female and (S or D)) = 	(M1)
=  or 0.333 (3 s.f.) or 33.3 % (3 s.f.)	(A1)	2
 
(ii)	P(Male and both D and S) = 	(M1)
=  or 0.4 or 40 %	(A1)	2
[14]

6.	(a)

(A1)

(A1)

2

(b)	P(J_1 Ç W) = , P(J_2 Ç W) = 	(M1)
Note: Award (M1) for either correct.
	P(W) = 	(M1)
=  or 0.467 (3 s.f.) or 46.7 % (3 s.f.)	(A1)	3
 
(c)	P(J_1 Ç W Ç W) = , P(J_2 Ç W Ç W) = 0	(M1)
P(W Ç W) = 
=  or 0.15 or 15%	(A1)	2
[7]

7.	
	(A4)	(C4)
Note: Award (A1) for each correct bold entry
[4]

8.	(a)	(i)	A = {2, 3, 5, 7, 11, 13}	(A1)
(ii)	B = {1,2, 3, 4, 6, 9, 12}	(A1)
(iii)	C = {4, 8, 12}	(A1)
(iv)	A Ç B Ç C = Æ	(A1)	4
 
(b)	(i)(ii)
	(A2)(A2)	4
	Also accept with elements
correctly placed
Note: Allow ft from part (a).
Award (A1) for rectangle labelled, (A1) for circles in correct places. Award (A1) for correct elements in intersections, award (A1) for the rest of the elements correctly placed. IF the wrong Universal set is used, penalise only one mark.
 
(c)	Note: Award follow through from part (b) only.
(i)	A Ç (B È C) = {2, 3}	(A1)
(ii)	(A Ç B)¢ = {1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}	(A1)
Note: Award follow through from part (c) (ii).
(iii)	(A Ç B)¢ Ç C = {4, 8, 12}	(A1)	3
 
(d)	Note: Award follow through from either part (a) or part (b).
(i)	 or 0.4 or 40%	(A1)
(ii)	 or 0.267 or 26.7% (3 s.f)	(A1)
Note: In parts (iii) and (iv), award (A1) for the correct numerator, (A1) for the correct denominator.
 
(iii)	or  or 0.4 or 40%	(A2)
(iv)	 or 0.286 or 28.6%(3 s.f.)	(A2)	6
[17]