Basic Probability: WJEC GCSE Intermediate November 2016 Unit 2 Q14

Intermediate November 2016 Unit 2 Q14

WJECIntermediateCurrent spec6 marksBasic Probability Sets

14. At a college, a total of 28 students study one or more of the science subjects: Biology, Chemistry and Physics.
The 28 students form the universal set, ε.
Some parts of the Venn diagram below have already been completed.

It is also known that:

5 students study only Biology
13 students study Chemistry

(a) Complete the Venn diagram. [3]

Venn diagram with universal set ε and three circles Biology, Chemistry and Physics; entries already filled: Biology and Chemistry only 2, Chemistry only 1, all three 6, Biology and Physics only 3, outside all circles 0; Biology only, Chemistry and Physics only, and Physics only are blank

(b) How many students study Biology and Chemistry but not Physics? [1]

Answer Venn diagram with circles B, C and P: 5 in Biology only, 4 in Chemistry and Physics only, 7 in Physics only — Mark scheme (a)

Scheme	Marks	Comments
Ribbon marking for 14(a), 14(b) and 14(c).
5 in correct position.	B1
4 in correct position.	B1
7 in correct position.	B1	Strict FT ‘their entries such that total number of students = 28. Allow ‘double entries’ in some parts for this FT, e.g. ‘the 4 placed alongside the 1’.

Mark scheme (b)

Scheme	Marks	Comments
Ribbon marking for 14(a), 14(b) and 14(c). 2	B1	Allow ‘double entries’ in some parts for a possible FT, e.g. ‘the 4 placed alongside the 2’.

Mark scheme (c)

Scheme	Marks	Comments
Ribbon marking for 14(a), 14(b) and 14(c). \(\dfrac{16}{28}\) or equivalent ISW	B2	FT ‘their total number for Biology’ for the numerator. Allow ‘double entries’. B1 for a correct numerator in a fraction <1. B1 for a denominator of 28 in a fraction <1. Penalise −1 for only words (16 out of 28) or only ratio (16:28).