Basic Probability: WJEC GCSE Intermediate November 2024 Unit 1 Q12

Intermediate November 2024 Unit 1 Q12

WJECIntermediateCurrent spec5 marksBasic Probability Pie Charts

12. The pie charts show the distributions of Year 7, Year 8 and Year 9 pupils in two schools, Ysgol Afon and Ysgol Twyn.

Ysgol Afon pie chart: Year 7 half, Year 9 and Year 8 a right angle each. Ysgol Twyn pie chart: Year 7 half, Year 9 60°, Year 8 the rest

There are 254 Year 7 pupils in Ysgol Afon.

The total number of pupils in Year 7, Year 8 and Year 9 in Ysgol Twyn is 480.

One pupil is chosen at random from all the Year 7, Year 8 and Year 9 pupils in these two schools.
What is the probability that this pupil is in Year 9? [5]

Mark scheme

Scheme	Marks	Comments
(Number of Year 9 pupils in Ysgol Afon = ) 127	B1	Answers may be seen on diagram Do not award B1 if 127 is clearly labelled as Year 7 Ysgol Afon.
(Number of Year 9 pupils in Ysgol Twyn = ) \(\frac{60}{360} \times 480\) or equivalent (e.g 480 ÷ 2 ÷ 3, 240 ÷ 3…)	M1	May be seen in stages.
80	A1	An answer of 80 implies M1A1.
(Total number of pupils = 508 + 480 =) 988 or (Total number of pupils = 494 + 287 + 207 =) 988	B1	CAO.
(Probability from Year 9 =) \(\dfrac{207}{988}\) ISW	B1	Sight of 207 implies the first B1 M1 A1. The numerator and denominator must both be integers for B1. FT \(\dfrac{\text{‘their 127’ + ‘their 80’}}{\text{’their 988’}}\), provided fraction <1 ‘their 988’ from ‘total for Ysgol Afon’ + 480 ‘their numerator’ is a sum of two values but NOT 90 + 60 (angles). Penalise incorrect notation -1 e.g. ‘207 in 988’. If no marks awarded, SC1 for engaging with the total number of pupils in Ysgol Afon. This could be sight of 508 or 254 + 254 or equivalent (seen or implied).