A 6 sided die is rolled 8 times. Each time, you record if the number is even or odd.

Question

A 6 sided die is rolled 8 times. Each time, you record if the number is even or odd.

a. How many different arrangements of evens and odds are there for these 8 rolls?

b. How many different ways can you get exactly 2 even numbers on these 8 rolls?

c. What is the probability that you will get exactly 2 even numbers on 8 rolls?

Answer 1

Rolling odd or even with a die is equivalent to flipping a coin, i.e. both are binomial trials with p=1/2.

a) 2⁸

b) ₈C₂

c) This answer should now be obvious!