Question

Determine whether or not the random variable X is a binomial random variable. If so, give the values of n and p . If not, explain why not.

1. X is the number of times the number of dots on the top face of a fair die is even in six rolls of the die.

2. X is the number of dice that show an even number of dots on the top face when six dice are rolled at once.

Answer 1

(1) Here, X is a binomial random variable because there are 2 outcomes - getting an even number or an odd number on the top face of a fair die, during 6 rolls of the die. Here, n = 6 and p = probability of getting an even number on the top face of the die = 0.5. Hence, X ~ Binomial(n = 6, p = 0.5).

(2) Here, X is a binomial random variable because there are 2 outcomes - getting an even number or an odd number on the top face of a fair die, when 6 dice are rolled at once. Here, n = 6 and p = probability of getting an even number on the top face of any die = 0.5. Hence, X ~ Binomial(n = 6, p = 0.5).