Question

A fair 6-sided die is rolled 4 times and the resulting sequence of 4 numbers is recorded. How many different sequences consist entirely of even numbers

Answer 1

81

Explanation:

Rolling 6-sided fair die you can throw out three even numbers: 2, 4, 6.

If a fair 6-sided die is rolled 4 times, then each of 4 times each of three even numbers can be thrown out. Then the number of different sequences that consist entirely of even numbers is

`3\cdot 3\cdot 3\cdot 3=3^4=81.`