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0580/21 Oct/Nov 2022, Question 25: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Calculator · 8 marks

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The question, in short

Bag has 5 red, 4 blue, 3 green balls. Find probabilities for random picks, expected count over 60 draws with replacement, probability of two different colours without replacement, and the pick number n where stopping on green has probability 21/220.

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

Part (ai) · 1 mark

Find the probability that a single random ball is red or blue.

  1. 1Red or blue = 5 + 4 = 9 balls
  2. 2P = 9/12 = 3/4

Answer3/4

Part (aii) · 1 mark

With replacement over 60 picks, calculate the expected number of times the ball is red or blue.

  1. 1Expected = 60 × 3/4
  2. 2= 45

Answer45

Part (b) · 4 marks

Two balls drawn without replacement; calculate the probability they are different colours.

  1. 1P(same colour) = 5/12 × 4/11 + 4/12 × 3/11 + 3/12 × 2/11
  2. 2= 20/132 + 12/132 + 6/132 = 38/132
  3. 3P(different) = 1 − 38/132 = 94/132
  4. 4= 47/66

Answer47/66

Part (c) · 2 marks

Without replacement, Marie stops at first green; given this probability is 21/220, find n.

  1. 19 balls are not green
  2. 2Pick 4: 9/12 × 8/11 × 7/10 × 3/9 = 7/55 = 28/220
  3. 3Pick 5: 9/12 × 8/11 × 7/10 × 6/9 × 3/8 = 21/220
  4. 4n = 5

Answer5

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Also searched as: 0580/21/O/N/22 · 0580_w22_qp_21 · 0580 w22 21 · question 25.
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