Question

Which of the following is TRUE for binomial distribution?
[Question ID = 1429]

• A. Binomial distribution is discrete in nature
• B. Binomial distribution has infinite events
• C. Binomial distribution has infinite outcomes
• D. Every trial is an independent trial

Hint:

Remember BINS:
B: Binary (2 outcomes).
I: Independent trials.
N: Number of trials is fixed.
S: Success probability ($p$) is constant for all trials.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question tests the fundamental assumptions of the Binomial Distribution, a probability distribution often used in genetics and population studies.

Step 2: Detailed Explanation:

• Binomial Distribution Properties: A binomial experiment consists of a fixed number of trials ($n$). Each trial has only two possible outcomes (success or failure).

• Independence (D): One of the most critical assumptions is that each trial is independent of the others. This means the outcome of one trial does not affect the probability of success in any other trial. (Option D is TRUE).

• Analyzing other options:
- Option (A): While the binomial distribution is indeed discrete, Option (D) is a more fundamental defining assumption for the probability formula to work.
- Option (B) and (C): These are false. Binomial distribution must have a finite number of trials ($n$) and exactly two outcomes per trial. If events were infinite, it might become a Poisson distribution.

Step 3: Final Answer:
In binomial distribution, every trial is an independent trial.