# Bernoulli Trials Probability Calculator

Calculator
Calculate the probability $$P(A)$$, where $$A$$ $$=$$ "there will exactly $$s$$ successes in $$t$$ trials".
 Number of trials $$t$$ Number of successes $$s$$ Probability of success $$p$$

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:

$$P(A) = \binom{5}{2} {1\over2}^2 {1 \over 2}^3 = 10 \times {1 \over 32} = 5/16 = 0.3125$$

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.