Higher June 2025 Paper 1 Q17
17 A bus is due to arrive at a bus stop at 1 pm
The probability that the bus is on time is halved when it is raining.
(a) Complete the tree diagram. [2 marks]
(b) Work out the probability that at 1 pm it is raining and the bus is not on time. [2 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{5}{6}\) Raining No and \(\dfrac{4}{13}\) Raining Yes, Bus on time Yes | B1 | |
| \(\dfrac{8}{13}\) Raining No, Bus on time Yes and \(\dfrac{5}{13}\) Raining No, Bus on time No | B1ft | both correct or ft \(2 \times\) their \(\dfrac{4}{13}\) and \(1 - (2 \times\) their \(\dfrac{4}{13})\) where their \(\dfrac{4}{13} \lt \dfrac{1}{2}\) |
Additional guidance
oe fractions, decimals or percentages throughout
| Answer | Mark | Comments |
|---|---|---|
| \(\dfrac{1}{6} \times \dfrac{9}{13}\) | M1 | oe may be seen on tree diagram |
| \(\dfrac{9}{78}\) or \(\dfrac{3}{26}\) | A1 | oe fraction, decimal or percentage |
Additional guidance
Ignore any attempt to simplify or convert after correct answer seen
There is no follow through for incorrect values