what is binomial distribution 
binomial distribution is a statistical distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters or assumptions the underlying assumptions of binomial distribution are that there is only one outcome for each trial each trial has the same probability of success and each trial is mutually exclusive or independent of one another understanding binomial distributionto start the binomial in binomial distribution means two terms the number of successes and the number of attempts each is useless without the other binomial distribution is a common discrete distribution used in statistics as opposed to a continuous distribution such as normal distribution this is because binomial distribution only counts two states typically represented as 1 for a success or 0 for a failure given a number of trials in the data binomial distribution thus represents the probability for x successes in n trials given a success probability p for each trial binomial distribution summarizes the number of trials or observations when each trial has the same probability of attaining one particular value binomial distribution determines the probability of observing a specific number of successful outcomes in a specified number of trials binomial distribution is often used in social science statistics as a building block for models for dichotomous outcome variables such as whether a republican or democrat will win an upcoming election whether an individual will die within a specified period of time etc it also has applications in finance banking and insurance among other industries analyzing binomial distributiona binomial distribution s expected value or mean is calculated by multiplying the number of trials n by the probability of successes p or n p for example the expected value of the number of heads in 100 trials of heads or tails is 50 or 100 0 5 another common example of binomial distribution is estimating the chances of success for a free throw shooter in basketball where 1 a basket made and 0 a miss the binomial distribution function is calculated as 