3p.06 Recognise that experimental probability will tend towards theoretical probability as... Quiz: Pearson Edexcel Statistics, Unit 3

The 20 questions

1. As the number of trials increases, experimental probability tends towards what?

   • Sample size
   • Theoretical probability
   • One
   • Zero

2. Which condition is required for experimental probability to tend towards theoretical probability?

   • No variation permitted
   • All variables are random
   • Fixed sample sizes
   • Exact outcomes known

3. Increasing the number of trials in an experiment generally leads to what?

   • Higher bias
   • Better probability estimates
   • Fewer outcomes
   • Exact certainty

4. What does the phrase 'tend towards' mean in experimental probability?

   • Remain completely constant
   • Get closer and closer
   • Drift away entirely
   • Reach zero instantly

5. A die is rolled 6 times and shows 3 sixes. What is the experimental probability of a six?

   • 3
   • 1/6
   • 0.5
   • 0.3

6. Why might a small number of trials produce misleading experimental probabilities?

   • Biased equipment
   • Chance variation
   • Fixed sample size
   • Poor experimental design

7. As trials increase, what does experimental probability do to theoretical probability?

   • Matches it instantly
   • Exceeds it
   • Ignores it
   • Approaches it

8. What is the primary benefit of increasing sample size in statistical estimation?

   • Zero error
   • Faster calculations
   • Removed randomness
   • Better probability estimates

9. Coin relative frequencies for 10, 100 and 1000 tosses are 0.6, 0.48 and 0.505. What happens?

   • Move closer to 1.0
   • Stay at 0.6
   • Move closer to 0.5
   • Become completely random

10. A spinner has P(blue) = 1/3. After 30 spins, 12 are blue. What happens with more spins?

    • Probability changes
    • Relative frequency nears 1/3
    • Frequency stays at 2/5
    • Blue becomes impossible

11. Which win probability estimate is more reliable: 7/10 or 480/1000?

    • Both equal reliability
    • Neither is reliable
    • 7 out of 10
    • 480 out of 1000

12. A relative frequency from 1000 trials is 0.25 for outcome X. What is the best estimate of its probability?

    • About 0.25
    • Exactly 250
    • Exactly 0.25 forever
    • About 0.75

13. Which action would most improve an estimate of a defect probability?

    • Stopping the trials
    • Ignoring random errors
    • Testing more items
    • Testing fewer items

14. Why might relative frequency vary greatly in early trials?

    • Biased equipment
    • Theoretical error
    • Incorrect formula
    • Small sample size

15. Which sample size gives a more stable probability estimate?

    • 40 trials
    • 1 trial
    • 10 trials
    • 4000 trials

16. What action reduces random variation in experimental probability estimates?

    • Changing the rule
    • Decreasing trials
    • Ignoring outliers
    • Increasing sample size

17. What does the law of large numbers state about relative frequency?

    • It approaches theoretical probability
    • It equals zero
    • It fluctuates wildly forever
    • It matches the median

18. How do relative frequencies typically behave as the number of trials increases?

    • They increase linearly
    • They settle down
    • They drop to zero
    • They become erratic

19. Why are random variables essential for experimental probability convergence?

    • Bias is eliminated
    • Outcomes become fixed
    • Trials happen faster
    • Chance balances out

20. Why can a small sample of 10 trials not confirm an exact probability?

    • Zero probability
    • High chance variation
    • Guaranteed bias
    • Perfect accuracy

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