Discia GCSE Maths › Probability › Probability Trees

Probability Trees 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 36 marks Sheet 1
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  1. 3 marks

    A bag contains 2 blue tiles and 7 grey tiles.

    A tile is taken from the bag at random, its colour is written down, and it is put back in the bag.

    A second tile is then taken from the bag at random.

    The tree diagram is not complete.

    A probability tree for two counters. The first pair of branches is labelled with probabilities and the second pair is blank.BlueGreyBlueGreyBlueGrey2979
    (a)

    State the probability that the second tile taken is grey.

    (b)

    Find the probability that both tiles taken are blue.

  2. 3 marks

    The probability that the train is late on Tuesday is \(0.4\).

    The probability that it is late on Wednesday is \(0.1\).

    The tree diagram shows this information. One probability is missing.

    A probability tree for two days, with one branch labelled with a question mark.LateOn timeLateOn timeLateOn time0.4?0.10.90.10.9
    (a)

    State the probability that should be written on the branch marked with a question mark.

    (b)

    Find the probability that the train is on time on both days.

  3. 4 marks

    Ben plays one game of tennis and one game of badminton.

    The probability that he wins the game of tennis is \(0.4\).

    The probability that he wins the game of badminton is \(0.6\).

    The two results are independent.

    A probability tree for two games, with the outcome of each path listed on the right.WinsLosesWinsLosesWinsLosesWins, WinsWins, LosesLoses, WinsLoses, LosesOutcome0.40.60.60.40.60.4
    (a)

    Find the probability that Ben wins both games.

    (b)

    Find the probability that Ben wins neither game.

  4. 3 marks

    On any Monday, the probability that Priya is late for school is \(\frac{ 3 }{ 8 }\).

    On the same Monday, the probability that Tomas is late for school is \(\frac{ 1 }{ 7 }\).

    Whether one of them is late does not affect the other.

    A probability tree with the first pair of branches for one person and the second pair for the other.Priya latePriya ontimeTomas lateTomas ontimeTomas lateTomas ontime385817671767

    Calculate the probability that exactly one of Priya and Tomas is late.

  5. 5 marks

    Hafsa takes three shots at a basketball hoop.

    The probability that she scores with any one shot is \(0.6\), and the shots are independent of each other.

    A three-level probability tree for three shots, each branching into scores and misses.ScoresMissesScoresMissesScoresMissesScoresMissesScoresMissesScoresMissesScoresMisses0.60.40.60.40.60.40.60.40.60.40.60.40.60.4
    (a)

    Find the probability that Hafsa scores with all three shots.

    (b)

    Find the probability that Hafsa scores with at least one of the three shots.

  6. 3 marks

    A bag contains 4 blue tiles and 3 grey tiles.

    A tile is taken from the bag at random, its colour is written down, and it is put back in the bag.

    A second tile is then taken from the bag at random.

    The tree diagram is not complete.

    A probability tree for two counters. The first pair of branches is labelled with probabilities and the second pair is blank.BlueGreyBlueGreyBlueGrey4737
    (a)

    Write down the probability that the second tile taken is grey.

    (b)

    Work out the probability that both tiles taken are blue.

  7. 3 marks

    The probability that the ferry is late on Tuesday is \(0.2\).

    The probability that it is late on Thursday is \(0.1\).

    The tree diagram shows this information. One probability is missing.

    A probability tree for two days, with one branch labelled with a question mark.LateOn timeLateOn timeLateOn time0.2?0.10.90.10.9
    (a)

    State the probability that should be written on the branch marked with a question mark.

    (b)

    Calculate the probability that the ferry is on time on both days.

  8. 4 marks

    Leila plays one game of darts and one game of snooker.

    The probability that she wins the game of darts is \(0.6\).

    The probability that she wins the game of snooker is \(0.4\).

    The two results are independent.

    A probability tree for two games, with the outcome of each path listed on the right.WinsLosesWinsLosesWinsLosesWins, WinsWins, LosesLoses, WinsLoses, LosesOutcome0.60.40.40.60.40.6
    (a)

    Calculate the probability that Leila wins both games.

    (b)

    Calculate the probability that Leila wins neither game.

  9. 3 marks

    On any Monday, the probability that Priya is late for school is \(\frac{ 6 }{ 7 }\).

    On the same Monday, the probability that Tomas is late for school is \(\frac{ 4 }{ 9 }\).

    Whether one of them is late does not affect the other.

    A probability tree with the first pair of branches for one person and the second pair for the other.Priya latePriya ontimeTomas lateTomas ontimeTomas lateTomas ontime671749594959

    Calculate the probability that exactly one of Priya and Tomas is late.

  10. 5 marks

    Amara takes three shots at a basketball hoop.

    The probability that she scores with any one shot is \(0.8\), and the shots are independent of each other.

    A three-level probability tree for three shots, each branching into scores and misses.ScoresMissesScoresMissesScoresMissesScoresMissesScoresMissesScoresMissesScoresMisses0.80.20.80.20.80.20.80.20.80.20.80.20.80.2
    (a)

    Calculate the probability that Amara scores with all three shots.

    (b)

    Calculate the probability that Amara scores with at least one of the three shots.

Answers

  1. (a) \(\frac{7}{9}\)
    (b) \(\frac{4}{81}\)
  2. (a) \(0.6\)
    (b) \(0.54\)
  3. (a) \(0.24\)
    (b) \(0.24\)
  4. \(\frac{23}{56}\)
  5. (a) \(0.216\)
    (b) \(0.936\)
  6. (a) \(\frac{3}{7}\)
    (b) \(\frac{16}{49}\)
  7. (a) \(0.8\)
    (b) \(0.72\)
  8. (a) \(0.24\)
    (b) \(0.24\)
  9. \(\frac{34}{63}\)
  10. (a) \(0.512\)
    (b) \(0.992\)

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