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4024/22 Oct/Nov 2023, Question 5: Tree Diagrams for Dependent Events

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 6 marks

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The question, in short

A bag has 40 balls, 28 red and the rest green; another has 9 blue and 7 yellow. Find probabilities, expected counts, complete a tree diagram, and find the probability of two same-colour balls.

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 ball from the 40-ball bag is green.

  1. 1Green balls = 40 − 28 = 12
  2. 2P(green) = 12/40

Answer12/40

Part (aii) · 1 mark

Find the expected number of green balls when the random draw is repeated 200 times with replacement.

  1. 112/40 × 200 = 60

Answer60

Part (bi) · 2 marks

Complete the tree diagram for two balls drawn without replacement from 9 blue and 7 yellow.

  1. 1First ball yellow: 7/16
  2. 2After blue: 15 left with 7 yellow, so yellow 7/15
  3. 3After yellow: 9 blue and 6 yellow of 15, so blue 9/15, yellow 6/15

AnswerCorrect tree diagram 7/16 on first branch 7/15 , 9/15 , 6/15 on second branches

Part (bii) · 2 marks

Find the probability that the two balls drawn without replacement are the same colour.

  1. 1P(both blue) = 9/16 × 8/15 = 72/240
  2. 2P(both yellow) = 7/16 × 6/15 = 42/240
  3. 3P(same colour) = 114/240 = 19/40

Answer19/40

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Also searched as: 4024/22/O/N/23 · 4024_w23_qp_22 · 4024 w23 22 · question 5.
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