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4024/12 Oct/Nov 2020, Question 15: Tree Diagrams for Independent Events

Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks

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The question, in short

Using a tree diagram for two bags (7 beads: 3 red, 4 white; 5 beads: 2 red, 3 blue), find probabilities of colour outcomes when one bead is drawn from each bag.

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

Part (a) · 1 mark

Find the probability that both beads drawn are red.

  1. 1P(red, red) = 3/7 × 2/5 = 6/35

Answer6/35

Part (b) · 1 mark

Find the probability that both beads drawn are white.

  1. 1The second bag has no white beads
  2. 2P(white, white) = 0

Answer0

Part (c) · 2 marks

Find the probability that exactly one of the two beads is red.

  1. 1P(red then blue) = 3/7 × 3/5 = 9/35
  2. 2P(white then red) = 4/7 × 2/5 = 8/35
  3. 3P(exactly one red) = 9/35 + 8/35 = 17/35

Answer17/35

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