What you’ll learn
Use simulation to estimate probability.
Key idea
An observed proportion estimates the modeled chance; the simulation must reproduce independent choices in separate slots.
Copying one draw produces dependence; observed proportions are finite estimates rather than theoretical guarantees.
Worked example
Enter the exact value or ordered values in the format requested below.
Uniform digits 0 through 9 encode success as [0, 1] and failure as [2, 3, 4, 5, 6, 7, 8, 9]. A trial succeeds only if both slots succeed. A record has 2 successful trials out of 40. Each slot is drawn independently. Enter the exact empirical probability from this record.
- Map uniform digits [0, 1] to success and [2, 3, 4, 5, 6, 7, 8, 9] to failure, drawing independently for both slots in each trial.
- Of 100 equally likely ordered digit pairs, 4 have both slots successful, giving model probability 1/25.
- The recorded 2 successful pairs in 40 trials give estimate 2/40=1/20; a finite estimate need not equal the model.
- Copying one draw makes slots dependent and both-success probability 1/5, not 1/25.
Answer: 1/20
Quick Check
Interpret the result of 'Use simulation to estimate probability' in the data-generating context, including units and population limits.
Uniform digits 0 through 9 encode success as [0, 1, 2, 3] and failure as [4, 5, 6, 7, 8, 9]. A trial succeeds only if both slots succeed. A record has 2 successful trials out of 20. Choose the valid simulation procedure and explain what its record estimates.