Practice Maths

Experimental vs Theoretical Probability — Solutions

Click any answer to watch the solution video.

  1. Six-sided die — theoretical probability

    1. P(even):
    2. P(>4):
    3. P(prime):
    4. P(7):
    5. P(<7):

  2. Drawing pin experiment

    1. P(point-up):
    2. P(point-down):
    3. Theoretical probability:
    4. Estimate in 500 drops:

  3. Counter bag experiment

    1. P(red):
    2. Expected red in 50:
    3. Expected blue in 50:
    4. Experimental P(red):
    5. Is 23 reasonable?:

  4. Biased spinner — 400 spins

    1. Total check:
    2. Experimental probabilities:
    3. Theoretical (fair):
    4. Sector favoured:

  5. Law of large numbers — coin flipping

    1. Experimental probabilities:
    2. Theoretical P(H):
    3. Trend:
    4. 10 trials not biased:
    5. Law of large numbers:

  6. Anya’s spinner — testing fairness

    1. Experimental probabilities:
    2. Expected frequency (fair):
    3. Greatest difference:
    4. Is it biased?:
    5. More confidence:

  7. Unknown marble ratio

    1. P(red) estimate:
    2. Estimated ratio red:blue:
    3. Estimated count in 20:
    4. Could theoretical P = 2/3?:
    5. Recommendation:

  8. Simulation of die rolling

    1. Expected frequency:
    2. P(even) experimental:
    3. P(even) theoretical:
    4. Comment:

  9. Canteen sandwich decision

    1. P(Brand A):
    2. Stock recommendation for 200:
    3. Critique of equal stocking:
    4. Expected Brand A among 60 students:

  10. Coin bias claim

    1. Experimental P(H):
    2. Theoretical P(H):
    3. Expected Heads in 20 flips:
    4. Why 13 doesn’t prove bias:
    5. 2000 flips, 1300 Heads: