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0580/12 May/Jun 2021, Question 19: Tree Diagrams for Independent Events

Cambridge IGCSE Mathematics 0580 · Paper 12 (Core) · Calculator · 4 marks

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The question, in short

A bag holds 5 red and 3 blue balls; Sophie draws one ball, replaces it, then draws again. Complete the tree diagram and find the probability both draws are blue.

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

Part (a) · 2 marks

Fill in the missing probabilities on the two-stage tree diagram for the first and second draws.

  1. 1P(blue) = 1 − 5/8 = 3/8 on the first branch
  2. 2The ball is replaced, so the second ball has the same probabilities.
  3. 3Second ball after Red: Red 5/8, Blue 3/8
  4. 4Second ball after Blue: Red 5/8, Blue 3/8

AnswerFirst ball: Blue 3/8. Second ball after Red: Red 5/8, Blue 3/8. Second ball after Blue: Red 5/8, Blue 3/8

Part (b) · 2 marks

Calculate the probability that both balls Sophie takes are blue.

  1. 1P(blue, blue) = 3/8 × 3/8
  2. 2= 9/64

Answer9/64

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Also searched as: 0580/12/M/J/21 · 0580_s21_qp_12 · 0580 s21 12 · question 19.
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