Imagine some experiment (for example, tossing a coin) that only has two possible outcomes. Such an experiment is called Bernoulli trial.
Now image a series of such experiments. What is the probability that tossing a fair coin 5 times we will get exactly 2 heads (and hence 3 tails)?
Let \(A\)— "There will be 2 heads in 5 trials". Then, the probability is given by:
Generally:
\( P(A) = \binom{n}{k} {p}^{n} {q}^{n-k} \)
Where
\(n\) is the number of trials;
\(k\) is the number of successes;
\(p\) the probability for a success;
\(q\) the probability for a failure;
and \(\binom{p}{q}\) is the binomial coefficient.