Binomial, Poisson, and Multinomial Distributions
The binomial distribution consists of the probabilities of each of the possible numbers of successes on trials for independent events that each have a probability of п (the Greek letter pi) of occurring. For the coin flip example, and . The formula for the binomial distribution is shown below:
where is the probability of successes out of trials, is the number of trials, and is the probability of success on a given trial. Applying this to the coin flip example,
If you flip a coin twice, what is the probability of getting one or more heads? Since the probability of getting exactly one head is and the probability of getting exactly two heads is , the probability of getting one or more heads is .
Now suppose that the coin is biased. The probability of heads is only . What is the probability of getting heads at least once in two tosses? Substituting into the general formula above, you should obtain the answer .64.