An independent trial is a repeated random experiment whose outcome probabilities remain unchanged across trials. In a binomial setting, each trial has two possible outcomes, such as success or failure, and the probability of success stays constant. section 3.1.2 section 3.4
Independent trials support binomial probability calculations when these conditions hold:
- The number of trials is fixed. section 3.1.2
- Each trial has two possible outcomes. section 3.4
- The probability of success remains the same for every trial. section 3.1.2
Computing a binomial probability
For 20 independent trials with a 0.5 success probability, the probability of exactly 7 successes is calculated as C(20, 7) × 0.5⁷ × 0.5¹³, producing 7.39288330078125%. With p = 0.2, SciPy's binom.pmf returns 5.454985048652523%. section 3.1.2
