where 
the mean of the binomial distribution is np and the variance of the binomial distribution is np 1 p when p 0 5 the distribution is symmetric around the mean such as when flipping a coin because the chances of getting heads or tails is 50 or 0 5 when p 0 5 the distribution curve is skewed to the left when p 0 5 the distribution curve is skewed to the right the binomial distribution is the sum of a series of multiple independent and identically distributed bernoulli trials in a bernoulli trial the experiment is said to be random and can only have two possible outcomes success or failure for instance flipping a coin is considered to be a bernoulli trial each trial can only take one of two values heads or tails each success has the same probability and the results of one trial do not influence the results of another bernoulli distribution is a special case of binomial distribution where the number of trials n 1 example of binomial distributionbinomial distribution is calculated by multiplying the probability of success raised to the power of the number of successes and the probability of failure raised to the power of the difference between the number of successes and the number of trials then multiply the product by the combination of the number of trials and successes for example assume that a casino created a new game in which participants can place bets on the number of heads or tails in a specified number of coin flips assume a participant wants to place a 10 bet that there will be exactly six heads in 20 coin flips the participant wants to calculate the probability of this occurring and therefore they use the calculation for binomial distribution the probability was calculated as 20 6 20 6 0 50 6 1 0 50 20 6 consequently the probability of exactly six heads occurring in 20 coin flips is 0 0369 or 3 7 the expected value was 10 heads in this case so the participant made a poor bet the graph below shows that the mean is 10 the expected value and the chances of getting six heads is on the left tail in red you can see that there is less of a chance of six heads occurring than seven eight nine 10 11 12 or 13 heads statcrunch binomial calculatorso how can this be used in finance one example let s say you re a bank a lender that wants to know within three decimal places the likelihood of a particular borrower defaulting what are the chances of so many borrowers defaulting that they would render the bank insolvent once you use the binomial distribution function to calculate that number you have a better idea of how to price insurance and ultimately how much money to lend out and keep in reserve 