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4024/21 Oct/Nov 2024, Question 11: Tree Diagrams for Dependent Events

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 7 marks

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The question, in short

Using a table of 25 shapes sorted by triangle/quadrilateral and line symmetry, find probabilities for drawing shapes under replacement and without replacement.

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

Part (a) · 2 marks

Find the probability that a randomly chosen triangle has line symmetry.

  1. 1Triangles: 4 + 5 = 9, with line symmetry: 4
  2. 2P(line symmetry) = 4/9

Answer4/9

Part (b) · 2 marks

Find the probability that two shapes drawn with replacement are both quadrilaterals.

  1. 1Quadrilaterals: 9 + 7 = 16 out of 25
  2. 2P(both) = 16/25 × 16/25 = 256/625

Answer256/625

Part (c) · 3 marks

Find the probability that exactly one of three shapes drawn without replacement is a triangle with line symmetry.

  1. 1Triangles with line symmetry: 4; other shapes: 21
  2. 2One order: 4/25 × 21/24 × 20/23 = 1680/13 800
  3. 3The triangle can be 1st, 2nd or 3rd: 3 × 1680/13 800 = 5040/13 800
  4. 4= 42/115

Answer42/115

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