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4024/22 Oct/Nov 2021, Question 6: Tree Diagrams for Dependent Events

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 7 marks

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The question, in short

Use a fair 8-sided spinner with scores 1, 2, 1, 2, 1, 6, 1, 2 and a bag of 7 red, 6 green and 3 white counters to find several probabilities.

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

Part (aia) · 1 mark

For one spin of the 8-sided spinner, find the probability that the score is 6.

  1. 1One of the 8 equal sectors shows 6
  2. 2P(6) = 1/8

Answer1/8

Part (aib) · 1 mark

For one spin of the 8-sided spinner, find the probability that the score is not 2.

  1. 1Three sectors show 2, so five do not
  2. 2P(not 2) = 5/8

Answer5/8

Part (aii) · 2 marks

For two spins of the 8-sided spinner, find the probability that both scores are 2.

  1. 1P(2) = 3/8 on each spin
  2. 2P(two 2s) = 3/8 × 3/8 = 9/64

Answer9/64

Part (b) · 3 marks

Leon takes two counters at random without replacement from 7 red, 6 green and 3 white; find the probability they are the same colour.

  1. 116 counters in total
  2. 2P(RR) = 7/16 × 6/15 = 42/240
  3. 3P(GG) = 6/16 × 5/15 = 30/240
  4. 4P(WW) = 3/16 × 2/15 = 6/240
  5. 5Total = 78/240 = 13/40

Answer13/40

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Also searched as: 4024/22/O/N/21 · 4024_w21_qp_22 · 4024 w21 22 · question 6.
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