Question

A fair die is rolled 5 times. What is the probability of having no 2 and no 4 among the rolls?

Answer 1

`32/243 ~~ 0.1317" "` or `" "13.17%`

Explanation:

In a single roll there are `6` equally possible outcomes, of which `4` are acceptable.

Hence the probability of no "2" or "4" in one roll is:

`4/6 = 2/3`

The probability of no "2" or "4" on each of the subsequent rolls is the same.

Hence the probability of no "2" or "4" on all of `5` rolls is:

`(2/3)^5 = 2^5/3^5 = 32/243 ~~ 0.1317`