Binomial Outcome – The term indicates two possibilities. One out of a defined two outcomes is possible in a Binomial Experiment.
Examples:
- Getting Head or Tail on flipping a coin;
- Scoring ‘Pass’ or ‘Fail’ marks in an examination
- Choosing ‘Male’ or ‘Female’ candidate
Binomial Distribution is the distribution of the row of outcomes in a sequential trial of Binomial experiments. The key parameters here are:
- The probability of success/failure a single Binomial Experiment (p, 1-p). We all know that if the probability of success is p, then the probability of the alternative i.e.: Failure is 1-p. In some cases, the probability of success and failure both may be equal, which is 0.5. In other cases it might differ. It is important that the p, 1-p should be constant/fixed for a Binomial Distribution.
- Number of trials involved in the Distribution function.
With the above two parameters we can calculate:
1. Probability of X number of successes out of N trials:
For example, the probability of selecting 5 women for 12 job openings can be calculated with the above formula. Assume, the probability of selecting a male candidate and female candidate is 0.5.
2. Cumulative Probability of getting up to X number of successes in N trials:
This is the probability of getting up to 5 women candidates. This can be calculated by summing up the probabilities of probabilities of getting 0, 1, 2…X successes. In our case it the sum of P(0),P(1),P(2),P(3),P(4) and P(5).