A binomial distribution refers to a probability distribution that deals with two outcomes of an event, i.e., success or no success. The occurrence of one event does not depend on the occurrence of the other, i.e., the events are independent in nature. Also, the number of times an event is repeated is fixed. It is closely related to Bernoulli distribution. The probability of success or P(S) for each trial is the same and the probability of failure of the trial or P(F) is equal to 1 – P(S).
Examples of Binomial Distribution
1. Testing a Drug
The binomial distribution is prominently used in the field of drugs and medicine. Whenever a new drug is invented to cure a particular disease, the effectiveness of the drug can be represented by two outcomes, i.e., whether the drug cures the disease or it does not. Also, the side effects of the drug can be measured in a similar manner. Either the drug causes side effects or it does not. Since the experiment has two possible results, i.e., a success or a failure, it can be represented with the help of binomial distribution.
2. Participating in a Lucky Draw
If you participate in a lucky draw contest, there exist two possible outcomes, i.e., you either win the contest or you lose the contest. Hence, one can easily express the probability of such an event as success or failure with the help of binomial distribution.
3. Estimate the Number of Fraudulent Transactions
Banks often make use of binomial distribution to estimate the chances that a particular credit card transaction is fraudulent or not. The total number of fraudulent transactions occurring in a particular area is recorded and fed as information or data to the binomial distribution calculator. The binomial distribution further helps to predict the number of fraud cases that might occur on the following day or in the future.
4. Number of Spam Emails Received
The prediction of the number of spam emails received by a person is one of the prominent examples of binomial distribution. This is because an email has two possibilities i.e., either it can be a spam e-mail or not.
5. Number of Shopping Returns
When a person shops a product, he/she is often provided with a choice of returning the product within the given time duration. The probability that the person will return the product can be represented with the help of binomial distribution. It helps the shopkeeper to estimate the number of shopping returns faced by the firm in the near future.
6. Questioning a Group of People about being Colour Blind
Suppose you pick a person out of a group of ten random strangers. The probability of that particular person suffering from colour blindness can be represented with the help of binomial distribution. This is because there are two possible outcomes of the experiment, i.e., either the person is colour blind representing the success of the event or the person is not colour blind representing the failure of the event.
7. Participating in an Election
If you participate in an election, the probability is that you can either win the election or you lose the election. Hence, the event can be easily represented with the help of a binomial distribution. A binomial distribution calculator can also be used to calculate the chances of a particular political party winning or losing an election provided the previous record of the party winning or losing the elections is already known.
8. Supporting a particular Sports Team
If you support a particular sports team in a game or an event, the chances of the event are that either your favoured team wins or loses the match. The two outcomes of the event represent the success or failure of the experiment therefore, the best-suited distribution in such a case is the binomial distribution. Similarly, binomial distribution can also be applied if you are playing a particular sport because there are two consequences of the event, i.e., either winning or losing.