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Bernoulli Trials

An experiment in which a single action, such as flipping a coin, is repeated identically over and over. The possible results of the action are classified as "success" or "failure". The binomial probability formula is used to find probabilities for Bernoulli trials.

Note: With Bernoulli trials, the repeated actions must all be independent.

 P(k successes in n trials) = $$\left( {\begin{array}{*{20}{c}}n\\k\end{array}} \right){p^k}{q^{n - k}}$$ n = number of trials k = number of successes n – k = number of failures p = probability of success in one trial q = 1 – p = probability of failure in one trial
 Example: You are taking a 10 question multiple choice test. If each question has four choices and you guess on each question, what is the probability of getting exactly 7 questions correct? n = 10 k = 7 n – k = 3 p = 0.25 = probability of guessing the correct answer on a question q = 0.75 = probability of guessing the wrong answer on a question P(7 correct guesses in 10 questions) = $$\left( {\begin{array}{*{20}{c}}{10}\\7\end{array}} \right){\left( {0.25} \right)^7}{\left( {0.75} \right)^3} \approx 0.0031$$