6. 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]
(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.
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