Let's Remember — Chapter Summary

Let's Remember

• Trials of a random experiment are Bernoulli trials if (i) each trial has exactly two outcomes, success or failure, and (ii) the probability of success remains the same in every trial.
• The probability of $x$ successes in $n$ Bernoulli trials is $P(x\text{ successes out of }n\text{ trials}) = \dfrac{n!}{x!(n-x)!}\,p^xq^{n-x} = {}^{n}C_x\,p^xq^{n-x}$, which is the $(x+1)$-th term of the binomial expansion $(q+p)^n$. …