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4024/21 May/Jun 2022, Question 7: Tree Diagrams for Independent Events

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 11 marks

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The question, in short

Use the given transport probabilities table to find p and combined probabilities, then use the grouped time data to complete a histogram and estimate overtime days.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

Find the missing probability p for bike, given the other three probabilities.

  1. 1p = 1 − (0.12 + 0.40 + 0.26)
  2. 2= 1 − 0.78 = 0.22

Answer0.22

Part (aii) · 2 marks

Find the probability that over two days he uses train one day and bus the other.

  1. 1P(train then bus) + P(bus then train) = 0.26 × 0.4 + 0.4 × 0.26
  2. 2= 2 × 0.104
  3. 3= 0.208

Answer0.208

Part (aiii) · 3 marks

Find the probability he uses the bus at least once across Wednesday and Thursday.

  1. 1P(not bus on one day) = 1 − 0.4 = 0.6
  2. 2P(no bus on either day) = 0.6 × 0.6 = 0.36
  3. 3P(bus at least once) = 1 − 0.36 = 0.64

Answer0.64

Part (bi) · 3 marks

Complete the histogram for the grouped times, using frequency density for the remaining intervals.

  1. 1Frequency density = frequency ÷ class width
  2. 27 < t ≤ 7½: 9 ÷ 0.5 = 18; 7½ < t ≤ 8: 23 ÷ 0.5 = 46
  3. 38 < t ≤ 8¾: 18 ÷ 0.75 = 24; 8¾ < t ≤ 10: 10 ÷ 1.25 = 8
  4. 4Draw the four bars on these bases with these heights

AnswerCorrect histogram drawn

Part (bii) · 2 marks

Estimate how many of the 70 days he works past 5.15 p.m., starting at 9.00 a.m.

  1. 19.00 a.m. to 5.15 p.m. is 8¼ hours, so overtime means t > 8.25
  2. 2From 8 < t ≤ 8¾: (0.5/0.75) × 18 = 24 × 0.5 = 12 days
  3. 3Plus all 10 days in 8¾ < t ≤ 10
  4. 412 + 10 = 22 days

Answer22

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Also searched as: 4024/21/M/J/22 · 4024_s22_qp_21 · 4024 s22 21 · question 7.
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