Answer to Question #103795 in Statistics and Probability for Katenda

Question

Which one of the following is not a property of a binomial distribution?
(1) Each experiment has n trials.
(2) The n trials are independent of each other.
(3) Each trial has two possible outcomes that are mutually exclusive i.e. a success and a failure
(4) The probability of success remains the same for all trials.
(5) The probability of success is always 1
2
because of there are two outcomes.

Answer 1

(5) The probability of success is always 1

2

because of there are two outcomes.

This is not correct about binomial distribution because the probability of success varies from experiment to experiment. For example when tossing a fair coin, probability of getting a head is 0.5. When tossing a biased coin, the probability of getting a head may be higher or lower depending on the position of bias. Also when rolling a fair dice if 1 was the target number then the probability of a success(getting a 1)would be 1/6.