Question

A six-sided number cube is rolled five times, X is the number of times an even number is rolled.

Which statement is true about this situation?


A. The variable X does not have a binomial distribution because P(success) is not constant.

B. The variable X has a binomial distribution. P(success)=0.5; number of trials = 5

C. The variable X does not have a binomial distribution because there are more than two possible outcomes.

D. The variable X has a binomial distribution. P(success)=0.2; number of trials = 5

Answer 1

It is B.

Explanation:

The probability of success of rolling an even number in 1 roll = 3/6 = 0.5. This is a constant and Probability of failure = 0.5. There are 2 possible outcomes so it is a Binomial Distribution.

Answer 2

Explanation:

A six sided die has three even numbers, and each roll is independent, so P(success) is constant at 3/6 = 0.5. Since it's constant, the variable X does indeed have a binomial distribution.

So the answer is the second one, which you have selected.