Question

Which of the following is the experimental condition in case of binomial distribution?

• A. The trials are dependent on previous trial
• B. The probability of success changes from trial to trial
• C. The number of trials are finite
• D. Each trial results in more than two outcomes

Hint:

Exam Tip:
Remember the acronym B.I.N.O.M.I.A.L.:
B - Binary outcomes (success/failure).
I - Independent trials.
N - Number of trials is fixed.
O - The probability of success is the same for each trial.
M - The number of successes is what we count.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, each with the same probability of success.

Step 2: Key Conditions for Binomial Distribution:
The conditions for a binomial experiment are:
• The experiment consists of a fixed number of trials (finite \(n\)).
• Each trial is independent.
• There are exactly two possible outcomes: success or failure.
• The probability of success (\(p\)) is constant for each trial.

Step 3: Analyzing the Options:

• (A) The trials are dependent on previous trial:
This is false. Trials must be independent.
• (B) The probability of success changes from trial to trial:
This is false. The probability must be constant.
• (C) The number of trials are finite:
This is true. The number of trials \(n\) is fixed and finite.
• (D) Each trial results in more than two outcomes:
This is false. Each trial must have exactly two outcomes.

Step 4: Final Answer:
Therefore, option (C) is correct.