◈ Oracle PrepSign Up Free
A-LevelMathematicsProbability and statistics9709/61 · May/June 2018 · Q68 Marks

Vehicles approaching a certain road junction from town A can either turn left, turn right or go straight on. Over time it has been noted that of the vehicles approaching this particular junction from town A, 55% turn left, 15% turn right and 30% go straight on. The direction a vehicle takes at the junction is independent of the direction any other vehicle takes at the junction.

  1. (i)Find the probability that, of the next three vehicles approaching the junction from town A, one goes straight on and the other two either both turn left or both turn right.[4]
  2. (ii)Three vehicles approach the junction from town A. Given that all three drivers choose the same direction at the junction, find the probability that they all go straight on.[4]

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

  1. [M1] P(SLL), P(SRR), P(SSL) or P(SSR) seen
  2. [A1] Two correct options 0.09075 or 0.00675 can be unsimplified
  3. [M1] Summing 6 prob options not all identical
  4. [A1] Correct answer
  5. [B1] (0.3)³ oe seen on its own as num or denom of a fraction
  6. [M1] Attempt at P(SSS+LLL+RRR) seen anywhere
  7. [A1] (0.15)³ + (0.55)³ + (0.3)³ oe seen as denom of a fraction
  8. [A1] Correct answer

Write your answer and get it marked

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.

Sign up free →

About this question

Topic
Probability and statistics, A-Level Mathematics (syllabus 9709). Structured question, 8 marks.
Source
A-Level Mathematics, May/June 2018 Paper 6 Variant 1, question 6.

Questions and mark schemes are from past examination papers and remain the copyright of the exam board. How Oracle Prep builds its content

Related Mathematics questions

Probability and statisticsFeb/Mar 201713m

The lengths, in centimetres, of middle fingers of women in Raneland have a normal distribution with mean u and standa…

Probability and statisticsFeb/Mar 20184m

A selection of 3 letters from the 8 letters of the word COLLIDER is made.

Probability and statisticsFeb/Mar 20186m

Last Saturday, Sarah recorded the colour and type of 160 cars in a car park. All the cars that were not red or silver…

AlgebraFeb/Mar 201810m

Let f(x) = (5x² + x + 27) / ((2x + 1)(x² + 9)).

Complex numbersFeb/Mar 201811m

The complex number 1 + 2i is denoted by u.

VectorsFeb/Mar 201811m

The line l has equation r = 4i + 3j – k + μ(i + 2j – 2k). The plane p has equation 2x – 3y – z = 4.

← Browse all past-paper questions

© 2026 Oracle Prep