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0580/41 Oct/Nov 2024, Question 5: Tree Diagrams for Independent Events

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 9 marks

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The question, in short

Box has 3 blue and 5 red pens; work out probabilities for single picks, two picks with replacement using a tree diagram, and three picks without replacement.

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

Part (a) · 1 mark

Find the probability that a single random pick from the box is red.

  1. 1P(red) = 5/8

Answer5/8

Part (bi) · 2 marks

Fill in the missing probabilities on the two-stage tree diagram for picks with replacement.

  1. 1The pen is replaced, so the probabilities are the same on both picks
  2. 2First pen: Blue 3/8, Red 5/8
  3. 3Second pen (after Blue and after Red): Blue 3/8, Red 5/8

AnswerTree diagram correct probabilities on 3 pairs of branches: Blue 3/8, Red 5/8

Part (bii) · 3 marks

Find the probability that the two pens picked with replacement are the same colour.

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

Answer17/32

Part (c) · 3 marks

Find the probability that 3 pens chosen without replacement contain 2 blue and 1 red.

  1. 1P(B, B, R) = 3/8 × 2/7 × 5/6 = 30/336
  2. 2There are 3 orders: BBR, BRB, RBB
  3. 3P = 3 × 30/336 = 90/336 = 15/56

Answer15/56

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Also searched as: 0580/41/O/N/24 · 0580_w24_qp_41 · 0580 w24 41 · question 5.
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