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0580/21 Oct/Nov 2025, Question 20: Tree Diagrams for Independent Events

Cambridge IGCSE Mathematics 0580 · Paper 21 (Extended) · Non-calculator · 9 marks

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The question, in short

Use the ball counts in bags A and B to work out probabilities for picking balls, completing a tree diagram, and handling a transferred ball.

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

Part (a) · 1 mark

Find the probability that two balls drawn without replacement from bag B are both black.

  1. 1Bag B has only 1 black ball, so two black balls cannot be picked
  2. 2P(both black) = 1/4 × 0/3 = 0

Answer0

Part (bi) · 2 marks

Fill in the missing probabilities on the tree diagram for picking from bag A then bag B.

  1. 1Bag A: black = 1 − 5/8 = 3/8
  2. 2Bag B (4 balls, 3 white, 1 black) after either branch: white 3/4, black 1/4

AnswerBag A: white 5/8, black 3/8 Bag B (after white): white 3/4, black 1/4 Bag B (after black): white 3/4, black 1/4

Part (bii) · 3 marks

Find the probability that the ball from bag A and the ball from bag B are the same colour.

  1. 1P(white, white) = 5/8 × 3/4 = 15/32
  2. 2P(black, black) = 3/8 × 1/4 = 3/32
  3. 3P(same colour) = 15/32 + 3/32 = 18/32

Answer18/32

Part (c) · 3 marks

Find the probability that the ball picked from bag B is black after one ball is moved from bag A.

  1. 1If white moved, bag B has 4 white and 1 black: P = 5/8 × 1/5 = 5/40
  2. 2If black moved, bag B has 3 white and 2 black: P = 3/8 × 2/5 = 6/40
  3. 3P(black from B) = 5/40 + 6/40 = 11/40

Answer11/40

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Also searched as: 0580/21/O/N/25 · 0580_w25_qp_21 · 0580 w25 21 · question 20.
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