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4024/21 Oct/Nov 2021, Question 5: Tree Diagrams for Dependent Events

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 8 marks

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The question, in short

From ten number cards, find probabilities for drawing even numbers with replacement, complete a tree diagram, and find the chance of one odd and one even; then find the probability of one yellow and one pink counter drawn without replacement from 5 yellow, 3 pink, 4 black.

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

Part (ai) · 1 mark

Find the probability that the first card drawn shows an even number.

  1. 1Even cards: 2, 2, 2, 4, 6, 8 → 6 out of 10
  2. 2P(even) = 6/10

Answer6/10

Part (aii) · 2 marks

Fill in all six missing probabilities on the tree diagram for two draws with replacement.

  1. 1First card: even 6/10, odd 4/10
  2. 2Second card on both branches: even 6/10, odd 4/10 (card replaced)

AnswerCorrect tree diagram

Part (aiii) · 2 marks

Calculate the probability of getting one odd number and one even number across the two draws.

  1. 1P(one odd, one even) = 6/10 × 4/10 + 4/10 × 6/10
  2. 2= 24/100 + 24/100 = 48/100 = 12/25

Answer12/25

Part (b) · 3 marks

Find the probability of drawing one yellow and one pink counter without replacement, giving the answer as a simplified fraction.

  1. 1P(Y then P) = 5/12 × 3/11 = 15/132
  2. 2P(P then Y) = 3/12 × 5/11 = 15/132
  3. 3Total = 30/132 = 5/22

Answer5/22

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Also searched as: 4024/21/O/N/21 · 4024_w21_qp_21 · 4024 w21 21 · question 5.
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