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4024/21 May/Jun 2024, Question 11: Tree Diagrams for Dependent Events

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

Use the January temperature probability 0.35 over 31 days, complete a two-day tree diagram, and find probabilities for two-day temperature outcomes; also find the probability two randomly chosen children from 14 wear different T-shirt colours.

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

Part (ai) · 1 mark

With 31 days and probability 0.35, work out the expected count of days above 14 °C.

  1. 10.35 × 31 = 10.85
  2. 2About 11 days (10 or 11)

Answer10 or 11

Part (aiia) · 2 marks

Fill the missing probabilities on the two-day tree diagram for above 14 °C and 14 °C or below.

  1. 1P(14 °C or below) = 1 − 0.35 = 0.65
  2. 2First day: 0.65; after Above: 0.65; after 14 °C or below: Above 0.35, 14 °C or below 0.65

AnswerCorrect tree diagram 0.65, 0.65, 0.35, 0.65

Part (aiib) · 1 mark

Using the tree, calculate the chance that both days are above 14 °C.

  1. 10.35 × 0.35 = 0.1225

Answer0.1225 or 49/400

Part (aiic) · 2 marks

Calculate the chance that exactly one of the two days is above 14 °C.

  1. 1Above then not, or not then above: 0.35 × 0.65 + 0.65 × 0.35
  2. 2= 2 × 0.2275 = 0.455

Answer0.455 or 91/200

Part (b) · 3 marks

From 14 children (8 red, 1 green, 5 blue), two are picked at random; find the chance their colours differ.

  1. 1P(same colour) = 8/14 × 7/13 + 5/14 × 4/13 + 1/14 × 0/13
  2. 2= 56/182 + 20/182 = 76/182
  3. 3P(different) = 1 − 76/182 = 106/182 = 53/91

Answer106/182 or 53/91

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