Subject: Mathematics
Book: Maths Mastery
The binomial distribution models the number of successes in n independent Bernoulli trials with probability p for each trial. The probability mass function is P(X=k)=C(n,k)p^k(1–p)^(n–k). For instance, the chance of 3 successes in 7 tries with p=0.4 can be computed directly from the formula. Graphically, it forms a discrete distribution with possible outcomes from 0 to n. This distribution is extensively used in quality testing, biology (genetic traits), and polling data (success/failure outcomes). Understanding its mean (np) and variance (np(1–p)) helps quantify uncertainty in repeated-trial contexts.
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