Higher June 2018 Paper 1 Q4

EdexcelHigherCurrent spec5 marksBasic Probability Sets

4 Here is a Venn diagram.

Venn diagram with three circles A, B and C in a universal set. A only: 6, 4, 2, 12. A and B: 1, 3. B only: 11, 7, 9. B and C: 5. C only: 10. A and C do not overlap. Outside all circles: 8

(a) Write down the numbers that are in the set

(i) \(A\)

(ii) \(B \cup C\) (2)

Brian writes down the statement \(A \cap C = \varnothing\)

(b) Is Brian’s statement correct?
You must give a reason for your answer. (1)

One of the numbers in the Venn diagram is picked at random.

Scheme	Marks
(i) 1, 2, 3, 4, 6, 12	B1
(ii) 1, 3, 5, 7, 9, 10, 11	B1
	(2)

Mark scheme (b)

Scheme	Marks
Yes with reason	B1
	(1)

Notes

B1: e.g. no numbers in both \(A\) and \(C\) or \(A\) and \(C\) do not intersect or \(A\) and \(C\) do not overlap or \(A\) and \(C\) are mutually exclusive

Mark scheme (c)

Scheme	Marks
	M1
\(\dfrac{10}{12}\) oe	A1
	(2)
	(5 marks)

Notes

M1: for 12 – 2 (=10) or \(\dfrac{a}{12}\) with \(a \lt 12\) or

10 and 12 used with incorrect notation E.g. 10 : 12

A1: for \(\dfrac{10}{12}\) oe or 0.83(3…) or 83(.3..)%