Binomial distribution: discrete probability distribution of the number of successes in a sequence of $n$ independent yes/no experiments, each of which yields success with probability $p$
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Null Hypothesis
Null hypothesis: there is no significant difference between specified populations, any observed difference being due to sampling or experimental error
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Binomial Distribution Formulas
$$P(X = k) = \binom{n}{k} p^k(1-p)^{n-k}$$
$$P(X \leq k) = \sum_{i=0}^{\lfloor k \rfloor} \binom{n}{i}p^i(1-p)^{n-i}$$