A-LevelMathematicsProbability and statistics9709/53 · Oct/Nov 2025 · Q14 Marks
There are a large number of students at Greenfield college. Each student travels to college by car, by bus or on foot, independently of any other student. The probability that any student travels by car is 0.4. The probability that any student travels by bus is 0.35.
- (a)3 students from Greenfield college are selected at random. Find the probability that none of these 3 students travel to college by car.[1]
- (b)11 students from Greenfield college are selected at random. Find the probability that fewer than 9 of these 11 students travel to college by car or by bus.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.
- [B1] (0.6)³ [= 0.216, 27/125] OE.
- [M1] One term of form ¹¹Cx (p)x(1-p)¹¹-x with 0<p<1,x≠0 or 11.
- [A1] Correct un-simplified expression, no terms omitted leading to final answer. Condone omission of final bracket '}' If other brackets omitted, allow recovery if 1 – 0.455 (or better) seen. Accept ¹¹Cx (p)x(1-p)¹¹-x with p = 0.75.
- [B1] 0.5445<p<0.545.
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