A-LevelMathematicsProbability and statistics9709/52 · May/June 2020 · Q25 Marks
A total of 500 students were asked which one of four colleges they attended and whether they preferred soccer or hockey. The numbers of students in each category are shown in the following table. | | Soccer | Hockey | Total | |:---|:---|:---|:---| | Amos | 54 | 32 | 86 | | Benn | 84 | 72 | 156 | | Canton | 22 | 56 | 78 | | Devar | 120 | 60 | 180 | | Total | 280 | 220 | 500 |
- (a)Find the probability that a randomly chosen student is at Canton college and prefers hockey.[1]
- (b)Find the probability that a randomly chosen student is at Devar college given that he prefers soccer.[2]
- (c)One of the students is chosen at random. Determine whether the events 'the student prefers hockey' and 'the student is at Amos college or Benn college' are independent, justifying your answer.[2]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] 56/500 or 14/125 or 0.112
- [M1] P(D∩S)/P(S) = 120/280
- [A1] 120/280 or 3/7
- [M1] P(H) × P(AUB) = P(H ∩ (A U B)) if independent
- [A1] 220/500 × 242/500 = 1331/6250 so not independent
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