Basic Probability: WJEC GCSE Intermediate November 2017 Unit 1 Q14

Intermediate November 2017 Unit 1 Q14

WJECIntermediateCurrent spec5 marksBasic Probability Sets

14. A group of pupils from a school took part in The Urdd National Eisteddfod.
All of them competed in at least one of the following competitions: Singing, Dancing or Reciting.

2 of them only took part in a Dancing competition.
5 only took part in a Reciting competition.
No one took part in both a Reciting and a Dancing competition.
3 took part in both a Singing and a Dancing competition.
9 took part in a Reciting competition.
22 took part in a Singing competition.

The Venn diagram below shows some of the above information.
The universal set, \(\varepsilon\), contains all of the pupils in the group.

One of the pupils in the group is chosen at random.
What is the probability that this person only took part in a Singing competition? [5]

Venn diagram with circles Singing, Dancing and Reciting in a universal set; 0 in the centre of all three, 2 in Dancing only, 0 outside the circles.

Completed Venn diagram: Singing only 15, Singing and Dancing only 3, Singing and Reciting only 4, Dancing and Reciting only 0, Reciting only 5. — Mark scheme

Scheme	Marks	Comments

5 AND 3 AND 0 in correct position.	B1	Allow empty space to imply 0.
Total of 9 for ‘Reciting’.	B1	C.A.O.
Total of 22 for ‘Singing’.	B1
(Probability only took part in ‘Singing’) = \(\dfrac{15}{29}\) ISW	B2	15/29 gains all 5 marks. Otherwise, strict F.T. from ‘their diagram'. B1 for a correct numerator in a fraction <1. B1 for a correct denominator in a fraction <1. Penalise -1 if incorrect notation used for probability e.g. ’15 out of 29’.