Tree Diagrams: WJEC GCSE Intermediate June 2024 Unit 1 Q15

Intermediate June 2024 Unit 1 Q15

WJECIntermediateCurrent spec4 marksTree Diagrams

15. A group of people hired two buses, Bus A and Bus B, to take them home from a party.
Bus A left the party at 11:00 p.m.
Bus B left the party at midnight.

A person from the group is chosen at random.
The probability that this person left the party on Bus A is \(\dfrac{3}{8}\).

The probability that this person sat on the left-hand side of the bus is equal to the probability that this person sat on the right-hand side.

(a) Complete the following tree diagram. [2]

Tree diagram: first branches Bus A (probability 3/8) and Bus B (blank); each bus then branches to Left-hand side and Right-hand side, all four probabilities blank

(b) What is the probability that this person sat on the right-hand side of the bus that left at midnight? [2]

Mark scheme (a)

Scheme	Marks	Comments
\(\dfrac{5}{8}\) on ‘Bus B’ branch.	B1	Numerator and denominator must be integers. Allow any equivalent to \(\dfrac{5}{8}\) e.g. 0·625. Do not allow 0·63.
\(\dfrac{1}{2}\) or \(\dfrac{4}{8}\) or 0·5 on all ‘seat branches’	B1	Allow any equivalent to \(\dfrac{1}{2}\).

Mark scheme (b)

Scheme	Marks	Comments
\(\dfrac{5}{8} \times \dfrac{1}{2}\) or equivalent	M1	FT ‘their \(\dfrac{5}{8}\)’ × ‘their \(\dfrac{1}{2}\)’ provided both values < 1.
\(= \dfrac{5}{16}\) or \(\dfrac{20}{64}\) or \(\dfrac{25}{80}\) or equivalent ISW	A1	Do not allow rounded or truncated answers if decimal given. Numerator and denominator must be integers.