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O-LevelMathematicsProbability4024/21 · May/June 2022 · Q711 Marks

(a) Yasir travels to work either by car, bus, train or bike. The probabilities of using these means of transport on any work day are shown in the table. [Table with Means of transport and Probability] (b) Yasir records the length of time he spends at work on each of 70 work days. The table shows the results. [Table with Time (t hours) and Frequency] (i) Complete the histogram to represent the data. [Figure showing histogram grid]

  1. (a)(i)Find p.[1]
  2. (a)(ii)Find the probability that on Monday and Tuesday he travels to work by train on one day and by bus on the other day.[2]
  3. (a)(iii)Find the probability that he travels to work by bus at least once on Wednesday or Thursday.[3]
  4. (b)(i)Complete the histogram to represent the data.[3]
  5. (b)(ii)Yasir starts work each day at 9.00 a.m. He is paid overtime if he works later than 5.15 p.m. Estimate the number of days he is paid overtime during these 70 work days.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

  1. [1] [0].22 oe
  2. [2] [0].208 oe
  3. M1 for 0.26 × 0.4 [× 2] oe
  4. [3] [0].64 oe
  5. M2 for 1 – 0.6×0.6 oe or 0.4×0.4 +0.4×0.6×2 oe
  6. or M1 for 0.6×0.6 oe seen or 0.4×0.6[×2] oe seen or 0.4×0.4 oe seen
  7. [3] Correct histogram drawn
  8. B1 for 3 more rectangles on correct bases
  9. B1 for 3 more correct frequency densities soi
  10. [2] 22
  11. M1 for 0.5×their24 +10 oe or 10 + (2/3) × 18 oe

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About this question

Topic
Probability, O-Level Mathematics (syllabus 4024). Structured question, 11 marks.
Source
O-Level Mathematics, May/June 2022 Paper 2 Variant 1, question 7.

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