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0580/43 May/Jun 2024, Question 9: Tree Diagrams for Dependent Events

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 12 marks

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The question, in short

From seven letter cards N, A, M, I, B, I, A, calculate probabilities for various random selections with and without replacement.

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

Part (ai) · 1 mark

Find the probability that a randomly chosen card shows the letter H.

  1. 1There is no card with H
  2. 2Probability = 0

Answer0

Part (aii) · 1 mark

Find the probability that a randomly chosen card shows the letter B.

  1. 11 card out of 7 shows B
  2. 2Probability = 1/7

Answer1/7

Part (b) · 2 marks

With replacement, find the probability that two random picks both show the letter I.

  1. 1P(I) = 2/7 each time (card replaced)
  2. 22/7 × 2/7 = 4/49

Answer4/49

Part (ci) · 3 marks

Without replacement, find the probability that two picks are one I and one N.

  1. 1I then N: 2/7 × 1/6 = 2/42
  2. 2N then I: 1/7 × 2/6 = 2/42
  3. 3Total = 4/42 = 2/21

Answer2/21

Part (cii) · 3 marks

Without replacement, find the probability that two picked cards show different letters.

  1. 1Same letters possible only for A A or I I
  2. 2P(AA) = 2/7 × 1/6 = 1/21, P(II) = 2/7 × 1/6 = 1/21
  3. 3P(different) = 1 − 2/21 = 19/21

Answer19/21

Part (d) · 2 marks

Cards are drawn without replacement until an A appears; given this probability is 4/21, find n.

  1. 1n = 1: 2/7 = 6/21; n = 2: 5/7 × 2/6 = 5/21
  2. 2n = 3: 5/7 × 4/6 × 2/5 = 40/210 = 4/21
  3. 3n = 3

Answer3

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Also searched as: 0580/43/M/J/24 · 0580_s24_qp_43 · 0580 s24 43 · question 9.
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