Binomial Distributions

According to Gerstman (2007 , a binomial event is that which has only two outcomes , and therefore if the probability for one of the outcomes is known , then the probability that the other outcome will occur is simply the difference of the known probability from 1 . Treating repeated trials as independent events , the compilation of results of a binomial experiment altering the number of desired successes while keeping the number of trials fixed forms a binomial distribution . The binomial probability distribution thus gives an idea of how likely it is that successive successes

can occur over a given number of trials . For say a simple experiment of throwing a fair coin 4 times , the probability of getting a heads in any toss is 0 .5 . Thus , the probability of getting no heads at all in the four tosses is 0 .5^4 while the probability of getting exactly 1 heads is 0 .5^2 , and the probability of getting 2 heads is 0 .5 and then the probability of getting more than 2 heads decreases in the same manner that the probabilities increased in the progression described . If the probabilities are altered in such a way that success is much more likely in a single event than failure , then given five trials it would be expected that having successive successes would be more probable than successive failures . The binomial distribution also allows probabilities for multiple events to simply be added in to give an idea of the total probability for that event...