A-level · Probability

Tree diagrams and sequential eventsExam-style questions

Using a tree diagram for two-stage experiments: multiply probabilities ALONG the branches of a path (AND), add across the paths that make up an event (OR), and use 1 − P(none) for "at least one". The crucial distinction between sampling WITH replacement (probabilities stay the same) and WITHOUT replacement (the totals, and so the later probabilities, change).

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12 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    A potter fires each vase in either a new kiln or an old kiln.
    • The probability that a randomly chosen vase is fired in the new kiln is pp
    • If a vase is fired in the new kiln, the probability that it cracks is 0.050.05
    • If a vase is fired in the old kiln, the probability that it cracks is 0.120.12
    The tree diagram below, where rr and ss are probabilities, shows this information.p1 − p0.05r0.12sNew kilnOld kilnCrackedNot crackedCrackedNot cracked(a) Complete the tree diagram by writing down the value of rr and the value of ss

    (1 mark)

    The probability that a randomly chosen vase cracks is 0.07450.0745
    (b) Find the value of pp

    (3 marks)
    (c) Find the probability that a randomly chosen vase is fired in the new kiln and does not crack.

    (2 marks)

    A vase is chosen at random and is found to have cracked.
    (d) Find the probability that this vase was fired in the old kiln.

    (2 marks)
    Level 3 · 8 marksTry it
  2. 2
    A bag contains 55 red and 33 blue counters. Two are drawn without replacement. Find the probability that both are red.
    Level 3 · 2 marksTry it
  3. 3
    A bag contains 55 red and 33 blue counters. Two are drawn without replacement. Find the probability of at least one red.
    Level 3 · 2 marksTry it
  4. 4
    A spinner lands on red with probability 0.40.4 each spin. It is spun twice. Find the probability of exactly one red.
    Level 3 · 2 marksTry it
  5. 5
    A bag contains 55 red and 33 blue counters. Three are drawn without replacement. Find the probability that all three are red.
    Level 3 · 2 marksTry it

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