Dice roll probability question

Question

Suppose I have a fair eight-sided die with three sides painted red and five sides painted blue, and roll it 4 times. Let X be the number of times the die lands with a red side facing up.

 

What is the Expected value of X and what is the variance of X?

Answer 1

This would be a binomial experiment

 

with n = 4

 

and p = 3/8

 

E(x) = np for a binomial

 

Variance of a binomial is np(1-p)

 

Therefore, E(x) = 4(3/8) = 1.5   (DO NOT ROUND)

 

Expected value does not need to be a possible value of the random variable

 

Variance = 4(3/8)(5/8) = .9375