Discia GCSE Maths › Probability › Conditional Probability

Conditional Probability worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 42 marks Sheet 1
Generate a different sheet
  1. 4 marks

    A bag contains 5 green cubes and 3 white cubes.

    Two cubes are taken from the bag at random, one after the other. The first cube is not put back before the second one is taken.

    The tree diagram is not complete.

    A probability tree for two counters taken without replacement, with the second pair of branches blank.GreenWhiteGreenWhiteGreenWhite5838
    (a)

    State the probability that the second cube is green, given that the first cube is green.

    (b)

    Work out the probability that both cubes are green.

  2. 3 marks

    A bag contains 5 red counters and 3 blue counters.

    Two counters are taken from the bag at random, one after the other, without replacement.

    A completed probability tree for two items taken without replacement, with the outcome of each path listed on the right.RedBlueRedBlueRedBlueRed, RedRed, BlueBlue, RedBlue, BlueOutcome583847375727

    Find the probability that the two counters are the same colour.

  3. 4 marks

    A bag contains 5 red pens and 4 black pens.

    Two pens are taken from the bag at random, one after the other, without replacement.

    A probability tree for two items taken without replacement, with the second pair of branches blank and the outcome of each path listed on the right.RedBlackRedBlackRedBlackRed, RedRed, BlackBlack, RedBlack, BlackOutcome5949

    Work out the probability that the two pens are different colours.

  4. 6 marks

    On any morning Callum walks to school.

    The probability that it rains is \(\frac{ 5 }{ 6 }\).

    If it rains, the probability that Callum is late is \(\frac{ 3 }{ 7 }\).

    If it does not rain, the probability that Callum is late is \(\frac{ 1 }{ 7 }\).

    A probability tree with rain on the first pair of branches and being late on the second, with different probabilities depending on whether it rained.RainNo rainLateOn timeLateOn time561637471767
    (a)

    State the probability that Callum is late, given that it rains.

    (b)

    Find the probability that it rains and Callum is late.

    (c)

    Find the probability that Callum is late.

  5. 4 marks

    A bag contains 5 winning tickets and 5 blank tickets.

    Three tickets are taken from the bag at random, one after the other, without replacement.

    A three-level probability tree for three counters taken without replacement.WinningBlankWinningBlankWinningBlankWinningBlankWinningBlankWinningBlankWinningBlank510510495959493858484848485838

    Calculate the probability that all three tickets are winning.

  6. 4 marks

    A bag contains 3 red cubes and 6 yellow cubes.

    Two cubes are taken from the bag at random, one after the other, without replacement.

    A completed probability tree for two items taken without replacement, with the probabilities written inline.RedYellowRedYellowRedYellow3/96/92/86/83/85/8

    Find the probability that at least one of the two cubes is red.

  7. 4 marks

    A bag contains 3 winning tickets and 5 blank tickets.

    Two tickets are taken from the bag at random, one after the other. The first ticket is not put back before the second one is taken.

    The tree diagram is not complete.

    A probability tree for two counters taken without replacement, with the second pair of branches blank.WinningBlankWinningBlankWinningBlank3858
    (a)

    State the probability that the second ticket is winning, given that the first ticket is winning.

    (b)

    Calculate the probability that both tickets are winning.

  8. 3 marks

    A bag contains 6 red pens and 4 black pens.

    Two pens are taken from the bag at random, one after the other, without replacement.

    A completed probability tree for two items taken without replacement, with the outcome of each path listed on the right.RedBlackRedBlackRedBlackRed, RedRed, BlackBlack, RedBlack, BlackOutcome61041059496939

    Work out the probability that the two pens are the same colour.

  9. 4 marks

    A bag contains 4 grey socks and 4 navy socks.

    Two socks are taken from the bag at random, one after the other, without replacement.

    A probability tree for two items taken without replacement, with the second pair of branches blank and the outcome of each path listed on the right.GreyNavyGreyNavyGreyNavyGrey, GreyGrey, NavyNavy, GreyNavy, NavyOutcome4848

    Work out the probability that the two socks are different colours.

  10. 6 marks

    On any morning Tomas walks to school.

    The probability that it rains is \(\frac{ 5 }{ 6 }\).

    If it rains, the probability that Tomas is late is \(\frac{ 6 }{ 7 }\).

    If it does not rain, the probability that Tomas is late is \(\frac{ 2 }{ 7 }\).

    A probability tree with rain on the first pair of branches and being late on the second, with different probabilities depending on whether it rained.RainNo rainLateOn timeLateOn time561667172757
    (a)

    Write down the probability that Tomas is late, given that it rains.

    (b)

    Calculate the probability that it rains and Tomas is late.

    (c)

    Calculate the probability that Tomas is late.

Answers

  1. (a) \(\frac{4}{7}\)
    (b) \(\frac{5}{14}\)
  2. \(\frac{13}{28}\)
  3. \(\frac{5}{9}\)
  4. (a) \(\frac{3}{7}\)
    (b) \(\frac{5}{14}\)
    (c) \(\frac{8}{21}\)
  5. \(\frac{1}{12}\)
  6. \(\frac{7}{12}\)
  7. (a) \(\frac{2}{7}\)
    (b) \(\frac{3}{28}\)
  8. \(\frac{7}{15}\)
  9. \(\frac{4}{7}\)
  10. (a) \(\frac{6}{7}\)
    (b) \(\frac{5}{7}\)
    (c) \(\frac{16}{21}\)

← All GCSE maths worksheets

{# Self-hosted. The public pages make no third-party request at all — see docs/PUBLIC_LAUNCH_HANDOFF.md before pointing this at a CDN again. #}