Tree Diagrams: WJEC GCSE Intermediate November 2017 Unit 2 Q16

Intermediate November 2017 Unit 2 Q16

WJECIntermediateCurrent spec5 marksTree Diagrams

16. All the members of a farming club visited the Royal Welsh Agricultural Show.
They all travelled to the show either by bus or by car.
None of them visited the show on more than one day.
The decision to travel by car or by bus was independent of the day of the visit.

A member of the club was selected at random.
The probability that this member travelled by bus was 0·87.

The probability that this member visited the show on the first day was \(\dfrac{2}{3}\).

(a) Complete the tree diagram shown below. [2]

Tree diagram: method of travel Bus (0·87) or Car (blank); then day of visit First day (2/3) or Other day (blank) on each branch

(b) What is the probability that a member, chosen at random, was not one of those who travelled by bus on the first day of the show? [3]

Mark scheme (a)

Scheme	Marks	Comments
0·13 on ‘car’ branch.	B1
1/3 on ‘other day’ branches.	B1	Do not penalise if one of branches left blank.

Mark scheme (b)

Scheme	Marks	Comments
\(1 - 0{\cdot}87 \times \dfrac{2}{3}\) OR \(0{\cdot}87 \times \dfrac{1}{3} + 0{\cdot}13 \times \dfrac{2}{3} + 0{\cdot}13 \times \dfrac{1}{3}\)	M2	M1 for sight of 0·87 × 2/3. F.T. ‘their 0·13’ and ‘their 1/3’.
= 0·42	A1	C.A.O. If M0 allow SC1 for sight of \(0{\cdot}13 \times \dfrac{2}{3}\) (= 0·0866..) seen in part (b). (This for travelling by car on the first day.)