Basic Probability: WJEC GCSE Higher June 2018 Unit 1 Q2

Higher June 2018 Unit 1 Q2

WJECHigherCurrent spec5 marksBasic Probability Sets

2. 30 rugby supporters travel to Cardiff on a coach.
They decide to investigate how many of them can sing one, or both, of the songs ‘Hen Wlad fy Nhadau’ and ‘Bread of Heaven’.

12 say they can sing both songs.
18 say they can sing ‘Bread of Heaven’.
5 say they cannot sing either of the songs.

(a) Complete the Venn diagram below to show this information.
The universal set, ε, contains all of the 30 supporters on the coach. [3]

Venn diagram: universal set rectangle with two overlapping circles labelled Hen Wlad fy Nhadau and Bread of Heaven

(b) One of these supporters is chosen at random.
What is the probability that this person can sing ‘Hen Wlad fy Nhadau’? [2]

Completed Venn diagram: HWN only 7, both 12, BoH only 6, outside 5 — Mark scheme (a)

Scheme	Marks	Comments
		Any ‘blank space’ to be taken as 0. If ‘notches/tallies’ are used, penalise −1 once.
12 AND 5 in correct position.	B1	B0 if any other number written in the same section.
Total of 18 for ‘Bread of Heaven’	B1	Allow more than one number in the same section.
Overall total of 30.	B1	Allow more than one number in the same section.

Mark scheme (b)

Scheme	Marks	Comments
\(\dfrac{19}{30}\) or equivalent. ISW	B2	B1 for a numerator of 19 OR FT ‘their total for HWN’ in a fraction < 1. B1 for a denominator of 30 OR FT ’their total’ in a fraction < 1. An answer of 19/30 gains B2 regardless of ‘their Venn diagram’. Penalise incorrect notation (e.g. ‘19 in 30’) −1.