Practice Maths

Two-Step Experiments and Tree Diagrams — Solutions

Click any answer to watch the solution video.

  1. Sample spaces

    1. Coin then 4-sided die:
    2. Die rolled twice:
    3. {A,B,C} then {1,2,3}:
    4. Spinner R/B spun twice:
    5. Marble {R,G,B} with replacement:
    6. {X,Y,Z} with replacement:

  2. Tree diagrams and probabilities

    1. P(two tails):
    2. P(at least one head):
    3. 3 flips, P(exactly two heads):
    4. Spinner R,B,G spun twice, P(same colour):

  3. Multiplication rule

    1. P(6 AND tails):
    2. P(red then blue), with replacement (3R, 5B):
    3. P(yellow then yellow), with replacement (4G, 6Y):
    4. Spinner 1–4 twice, P(sum = 5):
    5. P(even on die) × P(tails):

  4. Without replacement

    1. 3R 2B, 2 drawn, P(both red):
    2. P(one red one blue):
    3. 4 defective, 6 non-defective; P(both non-defective):
    4. 3 boys 2 girls, choose 2; P(both girls):

  5. Analysis

    1. Two dice, P(same number):
    2. Two dice, P(sum ≥ 10):
    3. Spinner 1–4 twice, P(product even):
    4. Subject × sport combinations:
    5. 2R 3B 1G (6 total), with replacement, P(at least one red):

  6. Problem solving

    1. Win: heads AND die > 4:
    2. Tuck shop (2 mains × 3 drinks):
    3. 5R 3B, two drawn without replacement:
    4. Lily’s claim:

  7. Colour bag — with and without replacement (4 red, 2 blue)

    1. (i) With replacement, P(two red):
    2. (ii) Without replacement, P(two red):
    3. (iii) Without replacement, P(exactly one blue):

  8. Board game spinner (1, 2, 3, 4 — spun twice, find totals)

    1. (i) Sample space size:
    2. (ii) P(total = 6):
    3. (iii) P(total is odd):
    4. (iv) P(total > 6):

  9. Three children

    1. (i) Sample space:
    2. (ii) P(all same gender):
    3. (iii) P(at least two girls):
    4. (iv) P(second child is a boy):

  10. Evaluate Sam’s claim (cards {1,2,3,4,5}; odd cards: 1,3,5)

    1. (i) With replacement, P(both odd):
    2. (ii) Without replacement, P(both odd):
    3. (iii) Is Sam correct?: