Question

Which of the following is not a characteristic of a binomial experiment? (1) The experiment consists of n identical trials. (2) The trials are independent. (3) Each trial results in one of two outcomes (commonly referred to as success, S, and failure, F). (4) The probability of success, P, should be close to 0.5.

Answer 1

The Binomial Distribution is a discrete distribution where there are two distinct possible outcomes defined as success or failure. The PDF for Binomial Distribution is ⁿC_x p^x(1-p)^n-x   where n is the number of trials and p is the probability of success. Value of p ranges from 0 to 1.

The characteristics of a Binomial Experiment are,

1) The experiment consists of 'n' identical trials.

2) The trials are indipendent. That is outcome of any one of the trials is not affected by the outcome of the others,.

3)Each trial results in one of the two outcomes(success or failure).

4) 'p' the probability of success should remain the same.

From the given 4 options in the question the fourth one is not a characteristic of a binomial experiment.

Option 4 is wrong since 'p' the probability of success can be any value from 0 to 1. That is 0<p<1. It is not neccessary that the value of 'p' should be close to 0.5.