The binomial distribution of probability can be used in order to find out the probability of successes when a number of independent trials are carried out, assuming that each success has the probability of taking place. There are four main conditions that can be derived from the above statement. They are:
Fixed number of trials
Two different classifications
Probability of success stays the same for all trials
It is necessary for all these conditions to be present in the process being investigated in order to make effective use of the formula of binomial probability distribution. Below is a more detailed look at each of these conditions.
The process that is under investigation needs to have a fixed number of trials and it is necessary that number of trials do not vary. The method for performing each trial must be the same; however there is a possibility that the results of the trials may vary.
It is also important that each of the trials must be independent. This implies that each trial should not have any sort of effect on the other trials. Some of the best examples of independent trials are rolling two dices or flipping a number of coins. Due to the events being independent, the multiplication rule can be used to multiply all the probabilities. A binomial distribution can also be used in cases where trials may not be technically independent.
There are two classifications under which each of the trials may be assembled successes and failures. Success may not always be something positive in terms of trials. A trial can be declared as a success if it manages to produce the expected results. For example, a trial is being conducted to determine the rate of failure of light bulbs. Success in this trial can be established if a bulb that does not work is found. On the other hand, if a light bulb works it would imply failure of the trial. The reason for defining successes and failures in this manner is that it may be favorable to emphasize on the low probability of a light bulb not working rather than the high probability of a light bulb working.
Throughout the process of investigation, it is important for the probabilities of successful trials to remain unchanged. A good illustration of this can be the process of flipping coins. The probability of flipping a head is 1/2 each time irrespective of the number of coins flipped. It is also possible for probabilities from each of the trials to differ slightly if sampling is done without substitution. However, this may not affect the usage of binomial distribution if the population is large enough.
Binomial distribution can be used in finding out the probabilities of an investigative study in various fields.