Under ideal conditions where recall outcomes are binary (remembered or forgotten), the distribution follows a binomial model. Utilizing frequency to estimate probability yields an unbiased estimate, with the primary source of error stemming from the variance of the binomial distribution.

• $Var(X) = N \cdot p \cdot (1-p)$
  • X represents the number of successes
  • N denotes the total number of trials
  • p denotes the true probability of success
• The average variance per experiment is $\cfrac{p(1 - p)}{N}$
• The standard deviation can be used to estimate the magnitude of error: $\sqrt{\frac{p(1-p)}{N}}$
• In the worst-case scenario, where p equals 0.5, the error is $\cfrac{1}{2\sqrt{N}}$

To achieve an error margin of 0.01 when p = 0.5, at least 2,500 trials are needed.