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4MA1/2HR Jan 2019, Question 15: Tree Diagrams for Independent Events

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks

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The question, in short

Barney throws a biased coin with heads probability 0.3 four times; find the probability of exactly 3 heads and of at least one head.

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

Part (a) · 3 marks

Calculate the probability that exactly 3 of the 4 throws land heads.

  1. 1P(not heads) = 1 − 0.3 = 0.7
  2. 2One order, e.g. HHHT: 0.3³ × 0.7 = 0.0189
  3. 3The tail can come in any of 4 places
  4. 44 × 0.0189 = 0.0756

Answer0.0756

Part (b) · 2 marks

Calculate the probability that the coin lands heads at least once in 4 throws.

  1. 1P(tails) = 1 − 0.3 = 0.7
  2. 2P(no heads in 4 throws) = 0.7⁴ = 0.2401
  3. 3P(at least one head) = 1 − 0.2401 = 0.7599

Answer0.7599

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