Subject: Mathematics
Book: Maths Mastery
Bernoulli trials describe experiments with exactly two outcomes (success or failure) in repeated independent trials. Each trial has probability p of success and q=1–p of failure. The probability of exactly k successes in n trials is given by C(n, k) × p^k × q^(n–k). For example, in 5 coin flips with p=0.5, the probability of exactly 2 heads is C(5,2) × 0.5² × 0.5³=10 × 0.25×0.125=0.3125. Bernoulli trials underpin binomial distributions, crucial for forecasting repeated events in manufacturing (defects), sales leads, and gambling odds. Familiarity fosters robust statistical analysis and real-life predictions.
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