In a random experiment, a collection of trials is called Bernoulli trials then which of the following statements are TRUE?
(A) The number of trials is infinite.
(B) Each trial has exactly two outcomes defined as success and failure.
(C) The trials are dependent by nature.
(D) The probability of success remains the same in each trial.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B) and (D) only
Trials of a random experiment are Bernoulli trials when: (i) the number of trials is finite; (ii) the trials are independent; (iii) each trial has exactly two outcomes, success or failure; (iv) the probability of success is the same in every trial.
So Bernoulli trials are finite in number and independent, each has exactly two outcomes, and the probability of success is the same in every trial.
Checking the statements
(A) The number of trials is infinite. — Incorrect. The number of trials is finite.
(B) Each trial has exactly two outcomes defined as success and failure. — Correct. This is condition (iii).
(C) The trials are dependent by nature. — Incorrect. The trials are independent.
(D) The probability of success remains the same in each trial. — Correct. This is condition (iv).
CBSE Applied Mathematics (Class XII):
Binomial Distribution
