In day to day life there are number of examples of binomial distribution like
1. exam result pass or fail
2. application reject or not reject
3.bus will come or not come
4.product defective or not defective
Binomial distribution has following characteristics
1.This distribution has only two possible outcomes for n number of trials like yes or no,go not go ,pass or fail,
More familiar example for binomial distribution is coin toss where only two possible outcomes are possible either Head or Tail for n number of trials
2. Trails are fixed say “n “ numbers and all are identical.
3.Probability of success (p) remains constant from trial to trial
4. Result of each trial is independent of other trial.
Example:Suppose in exam there are 10 questions and each question has four possible answers out of which only one is correct then probability of any answer being correct is 1/4=0.25 - This probability of correct answer will be same for each question.
To calculate the probability of all answers being correct:
probability of success on single trial = 0.25
Trials = 10
Successes = 10