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?

Answer 1

The first statement is correct.

Explanation:

Let's first see if there is a binomial distribution, then if there is let's set it up.

A binomial distribution is one where there are 2 possible outcomes in a given set of trials (say even and odd results on a die), the probability of success is fixed (say like `1/2` for rolling an even number), and there is a fixed number of trials (say like 5).

A general statement about binomial distributions is:

`sum_(k=0)^(n)C_(n,k)(p)^k(1-p)^(n-k)=1`

with X being the number of times an even is rolled, we have:

`C_(5,X)(1/2)^X(.5)^(5-X)`

The right statement is the first one - X has a binomial distribution with P(success)=0.5 and trials = 5.