# Which of the following is not a requirement of the binomial probability distribution?

-Which of the following is not a requirement of the binomial probability distribution?
– Each attempt must have all outcomes organized into two categories.
– The attempt must be dependent.
– The probability of success remains the same in all attempts.
– The procedure has a fixed number of attempts.

This problem aims to discuss the requirements of the binomial probability distribution and choose which of the options is correct. Let’s first discuss what exactly is a binomial probability distribution.

The binomial probability distribution is a distribution that builds the possibility that a given set of parameters will have one or two independent states. The assumption here is that there is only one outcome for every trial or spin and that each trial is completely distinguished from one other.

Oftentimes we face circumstances where there are only two outcomes of interest, like flipping a coin to produce heads or tails, endeavoring a free throw in basketball that will either be successful or not and grade testing of parts. In each circumstance, we can relate the two results as either a hit or a defeat, depending on how the experiment is defined.

###### The answer to the problem is $B$, but first, let’s get deep into it.

Whenever these four specific conditions discussed below are fulfilled in an experiment, it is called a $Binomial$ set which will produce a $Binomial Distribution$. The four requirements are:
1)  Every observation should be categorized into two possibilities as success or failure.
2)  There can only be a designated number of observations.
3)  All observations are independent of one another.
4)  All observations are likely to have the same success probability – equally likely.

As we can see that in the correct requirements, all the observations or trials must be independent of one another so that the result of any particular trial does not affect the result of any other trial.

## Numerical Result:

Option $B$ can’t be a requirement of the binomial distribution and it is the correct answer.

## Example:

Assume that you are given a $3$ question MCQ test. Each question has $4$ answers, and only one is correct. Is This a binomial probability distribution problem?

• The number of questions is 3, and each question is itself a trial, so the number of trials is fixed. In this case, $n = 3$.
• If we get the first question to be correct, it will have no effect on the second and the third question, so all the trials are independent of one another.
• You can only guess the question to be right or wrong, eliminating the possibility of getting a third option, so there can only be two outcomes. In this case, the success would be if the question is right.
• Since there are four questions, the probability of getting a question right would be $p = \dfrac{1}{4}$. This would be the same for every trial since each trial has $4$ responses.

This is a binomial probability distribution since all of the properties are met.