Practice Maths

Multi-Step Probability and Tree Diagrams — Solutions

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  1. Marble bag with replacement

    1. Tree diagram:
    2. Sample space:
    3. P(Red, Red):
    4. P(at least one Blue):
    5. P(both same):

  2. Two fair coins

    1. Sample space:
    2. P(HH):
    3. P(exactly one Tail):
    4. P(at least one Head):

  3. Spinner then die

    1. Sample space size:
    2. P(2 and 5):
    3. P(same number):
    4. P(sum > 7):

  4. Electives and languages

    1. Combinations:
    2. P(Art and French):
    3. P(Drama or Music, any language):
    4. P(not Sport, Spanish):

  5. Balls without replacement

    1. Tree diagram:
    2. P(GG):
    3. P(one of each):
    4. P(at least one Y):
    5. Comparison:

  6. Three coin flips

    1. Sample space size:
    2. P(HHH):
    3. P(exactly two Heads):
    4. P(at least one Tail):
    5. P(H first | other two are T):

  7. Five-card draw without replacement

    1. P(Ace first):
    2. P(Ace second | Ace first):
    3. P(Ace both draws):
    4. P(sum > 7):
    5. P(at least one odd, Ace=1):

  8. Class representatives

    1. P(both girls):
    2. P(both boys):
    3. P(one of each):
    4. Verify sum = 1:

  9. Factory light bulbs

    1. Tree diagram:
    2. P(both defective):
    3. P(exactly one defective):
    4. P(at least one not defective):
    5. P(batch passed):

  10. Weather and cricket

    1. Tree diagram:
    2. P(rain and practice):
    3. P(plays cricket and no extra practice):
    4. Expected points: