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4024/21 Oct/Nov 2022, Question 5: Tree Diagrams for Dependent Events

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

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The question, in short

Compare the chance of drawing a black ball from two bags with given white and black counts, predict white draws over 220 trials with replacement, then complete a tree diagram for drawing two counters without replacement and find a probability.

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

Part (ai) · 2 marks

Using 5 white and 4 black in bag 1, and 6 white and 5 black in bag 2, show that a black ball is more likely from bag 2.

  1. 1P(black from bag 1) = 4/9 = 0.444…
  2. 2P(black from bag 2) = 5/11 = 0.454…
  3. 30.454… > 0.444…, so George is correct

AnswerCorrect justification with probabilities 0.44… and 0.45… seen

Part (aii) · 2 marks

From bag 2 with 6 white and 5 black, find the expected number of white balls in 220 draws with replacement.

  1. 1P(white from bag 2) = 6/11
  2. 2Expected number = 6/11 × 220 = 120

Answer120

Part (bi) · 2 marks

For 7 blue, 6 red and 3 green counters drawn twice without replacement, fill in the missing second-draw fractions on the tree diagram.

  1. 1After blue (6 blue, 6 red, 3 green left): red 6/15, green 3/15
  2. 2After red (7 blue, 5 red, 3 green left): red 5/15, green 3/15
  3. 3After green (7 blue, 6 red, 2 green left): red 6/15, green 2/15

AnswerCorrect tree diagram 6/15, 3/15, 5/15, 3/15, 6/15, 2/15

Part (bii) · 3 marks

With 7 blue, 6 red and 3 green counters, two drawn without replacement, find the probability that at least one counter is red.

  1. 1P(no red) = 10/16 × 9/15 = 90/240 = 3/8
  2. 2P(at least one red) = 1 − 3/8 = 5/8

Answer5/8

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Also searched as: 4024/21/O/N/22 · 4024_w22_qp_21 · 4024 w22 21 · question 5.
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