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0580/43 Oct/Nov 2024, Question 9: Tree Diagrams for Independent Events

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 9 marks

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The question, in short

Bag has 5 white and 3 black balls; find probabilities for random picks with and without replacement, including expected count over 120 draws.

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

Part (ai) · 1 mark

Find probability a single random ball, replaced after picking, is white.

  1. 15 white out of 8 balls
  2. 2P(white) = 5/8

Answer5/8

Part (aii) · 1 mark

Find expected number of white balls when a random pick is repeated 120 times with replacement.

  1. 1Expected = 120 × 5/8
  2. 2= 75

Answer75

Part (bi) · 3 marks

Find probability two random picks with replacement give balls of the same colour.

  1. 1P(WW) = 5/8 × 5/8 = 25/64
  2. 2P(BB) = 3/8 × 3/8 = 9/64
  3. 3P(same) = 34/64 = 17/32

Answer17/32

Part (bii) · 1 mark

Find probability two random picks with replacement give balls of different colours.

  1. 1P(not same) = 1 − 17/32
  2. 2= 15/32

Answer15/32

Part (c) · 3 marks

Find probability that 3 balls picked without replacement contain two white and one black.

  1. 1P(W, W, B) = 5/8 × 4/7 × 3/6 = 60/336
  2. 2The black ball can be 1st, 2nd or 3rd: 3 orders
  3. 3P = 3 × 60/336 = 180/336 = 15/28

Answer15/28

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Also searched as: 0580/43/O/N/24 · 0580_w24_qp_43 · 0580 w24 43 · question 9.
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