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0580/31 May/Jun 2021, Question 2: Pie Charts

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 9 marks

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The question, in short

Use a frequency table of marbles for 15 friends to complete sector angles and a pie chart, then compare black-marble probabilities for bags A and B and find added marbles.

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

Part (ai) · 2 marks

Calculate the pie chart sector angle for each marble-count group and fill in the table.

  1. 1360 ÷ 15 = 24° per friend
  2. 20: 2 × 24 = 48°
  3. 31 to 10: 8 × 24 = 192°
  4. 411 to 50: 4 × 24 = 96°, more than 50: 1 × 24 = 24°

Answer| Number of marbles | Pie chart sector angle | | 0 | 48 | | 1 to 10 | 192 | | 11 to 50 | 96 | | More than 50 | 24 |

Part (aii) · 2 marks

Draw the remaining pie chart sectors using the angles found, starting from the given radius.

  1. 1Start at the vertical radius and measure each angle with a protractor.
  2. 2Draw sectors of 48°, 192°, 96° and 24° (total 360°).
  3. 3Label each sector with its number of marbles.

AnswerCorrect pie chart

Part (bi) · 1 mark

State the probability that a random marble from bag A is black.

  1. 1Bag A has 2 + 3 = 5 marbles, 2 black
  2. 2P(black) = 2/5

Answer2/5

Part (bii) · 2 marks

Judge whether Toby's claim about bag B giving a higher black probability is correct, with a reason.

  1. 1P(black from A) = 2/5 = 0.4
  2. 2P(black from B) = 5/(5 + 8) = 5/13 ≈ 0.385
  3. 30.385 < 0.4, so Toby is not correct: black is less likely from bag B

AnswerNo, P(black from B) = 5/13 ≈ 0.385, which is less than P(black from A) = 2/5 = 0.4

Part (biii) · 2 marks

Find the smallest numbers of black and white marbles added to bag B so both bags have equal black probability.

  1. 1Bag B needs P(black) = 2/5, e.g. 6 black out of 15 marbles (6/15 = 2/5)
  2. 26 − 5 = 1 black added, 15 − 6 − 8 = 1 white added
  3. 3Black 1, White 1

AnswerBlack 1, White 1

Stuck on a step? Read the free lesson: Pie Charts

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Also searched as: 0580/31/M/J/21 · 0580_s21_qp_31 · 0580 s21 31 · question 2.
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