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Cambridge IGCSE Mathematics practice

exam practice - Calculate the probability of combined events, which may include scenarios with or without replacement. This can be represented using sample space diagrams, Venn diagrams (where the notation P(A ∩ B) and P(A ∪ B) can be applied), and tree diagrams, where outcomes are indicated at the ends of branches and probabilities are noted alongside the branches. - Probability of combined events

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Probability of combined events

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Paper 2Core or Extended Mathematics3 marks

A box contains 4 green marbles and 3 yellow marbles. Two marbles are drawn one after the other without replacement.

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Probability without Replacement

Calculate the probability of drawing a green marble followed by a yellow marble from a box containing 4 green marbles and 3 yellow marbles, without replacement.

  1. a

    Calculate the probability of drawing a green marble on the first draw.

    Aim for approximately 1 distinct marking point.

    [1]
  2. b

    Calculate the probability of drawing a yellow marble on the second draw after a green marble has been drawn.

    Aim for approximately 2 distinct marking points.

    [2]

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  • Topic focus: Probability of combined events.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
  • Check the operation, notation, units, and final answer form against the question before moving on.

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Paper 2 structured question: Probability of combined events

Paper 2Core or Extended Mathematics3 marks

Description

Probability with Replacement

Calculate the probability of drawing two red balls in succession from a bag containing 3 red balls and 2 blue balls, with replacement.

  1. a

    Calculate the probability of drawing a red ball on the first draw.

    Aim for approximately 1 distinct marking point.

    [1]
  2. b

    Calculate the probability of drawing two red balls in succession.

    Aim for approximately 2 distinct marking points.

    [2]