Question

A 6 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?



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

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

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

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

Answer 1

Option 3 -The variable X has a binomial distribution. P(success)=0.5; number of trials = 5

Explanation:

Given : A 6 sided number cube is rolled five times, X is the number of times an even number is rolled.

To find : Which statement is true about this situation?

Solution :

We have seen the situation is of binomial distribution,

The binomial distribution is defined as,

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

with X being the number of times an even is rolled

and there are 2 possible outcomes in a given set of trials (say even and odd results on a die), the probability of success is
`(1)/(2)`

and there is a fixed number of trials (say like 5).

So, the binomial is

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

Therefore, Option 3 is correct.

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