Consider an experiment that involves repeatedly rolling a six-sided die. Which of the following is a binomial random variable?
A) The number of rolls until a "4" is rolled for the first time.
B) The number of times that a "4" is rolled when the die is rolled six times.
C) The sum of the numbers observed on the first six rolls.
D) It is not possible to have a binomial random variable when rolling a six-sided die because a binomial random variable allows only two possible outcomes, not six.

Question

Quizplus · Accepted Answer

A binomial random variable is defined by having a fixed number of trials (in this case, six rolls), two possible outcomes (rolling a "4" or not rolling a "4"), and a constant probability of success on each trial (1/6 chance of rolling a "4"). Option B meets these criteria, making it a binomial random variable.

Consider an Experiment That Involves Repeatedly Rolling a Six-Sided Die