A-LevelMathematicsProbability and statistics9709/52 · May/June 2025 · Q46 Marks

Vehicles approaching a certain road junction from Bromley must go either left, right or straight on. Over time, it is known that 30% turn left, 25% turn right and 45% go straight on. The driver of each vehicle chooses a direction independently of all other drivers.

(a)Find the probability that the next three vehicles approaching this junction from Bromley all go in different directions.[2]
(b)Find the probability that, from the vehicles approaching this junction from Bromley today, the 1st vehicle to go left is before the 9th vehicle.[2]
(c)Find the probability that, from the vehicles approaching this junction from Bromley today, the 2nd vehicle to go left is the 7th vehicle.[2]

Mark scheme

Marking points from the official mark scheme (May/June 2025). The mark or mark type is shown in brackets.

[M1] OE. 0.3×0.25×0.45×k, k an integer > 1. E.g. 6 = 3! = 3P3 etc.
[A1] CAO exact answer.
Method 1: [M1] 1–0.7d, d = 8, 9, 0.75, 0.3 are not misreads. [A1] 0.942 <p<0.9425.
Method 2: [M1] 0.3+0.3(0.7)+0.3(0.7)² +0.3(0.7)³ +0.3(0.7)⁴ + 0.3(0.7)⁵ +0.3(0.7)⁶ +0.3(0.7)⁷ [+0.3(0.7)⁸]. [A1] 0.942 <p<0.9425.
[M1] (p)² (1-p)k ×k, 0<p<1,k = 5 or 6 .
[A1] AWRT.

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