Question:
Which of the following is not a property of a Binomial distribution?
Which of the following is not a property of a Binomial distribution?
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For a binomial distribution:
\[
n=\text{fixed},\quad p=\text{constant},\quad \text{trials independent}
\]
and each trial has only two outcomes: success or failure.
Updated On: Jun 22, 2026
- Random experiment consists of a sequence of \(n\) identical trials
- Each outcome can be referred to as a success or a failure
- The probabilities of the two outcomes can change from one trial to the next
- The trials are independent
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The Correct Option is C
Solution and Explanation
Step 1: Recall the properties of a Binomial distribution.
A binomial distribution is based on a binomial experiment having the following properties:
(i) A fixed number of trials (ii) Trials are independent (iii) Each trial has only two outcomes: success or failure (iv) Probability of success remains constant in every trial
Step 2: Examine each option.
Option (1): Random experiment consists of identical trials This is a correct property of a binomial experiment.
Option (2): Each outcome can be classified as success or failure This is also a correct property.
Option (4): The trials are independent This is again a standard property of the binomial distribution.
Option (3): The probabilities of the two outcomes can change from one trial to the next This is incorrect because in a binomial distribution, the probability of success \(p\) and failure \(q\) remains constant for every trial.
Therefore, this statement is not a property of a binomial distribution.
Step 3: Final conclusion.
Hence, the statement which is not a property of a binomial distribution is \[ \boxed{\text{The probabilities of the two outcomes can change from one trial to the next}} \] which corresponds to option (3).
A binomial distribution is based on a binomial experiment having the following properties:
(i) A fixed number of trials (ii) Trials are independent (iii) Each trial has only two outcomes: success or failure (iv) Probability of success remains constant in every trial
Step 2: Examine each option.
Option (1): Random experiment consists of identical trials This is a correct property of a binomial experiment.
Option (2): Each outcome can be classified as success or failure This is also a correct property.
Option (4): The trials are independent This is again a standard property of the binomial distribution.
Option (3): The probabilities of the two outcomes can change from one trial to the next This is incorrect because in a binomial distribution, the probability of success \(p\) and failure \(q\) remains constant for every trial.
Therefore, this statement is not a property of a binomial distribution.
Step 3: Final conclusion.
Hence, the statement which is not a property of a binomial distribution is \[ \boxed{\text{The probabilities of the two outcomes can change from one trial to the next}} \] which corresponds to option (3).
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