If a fair die is rolled three times, what is the probability

[BTGmoderatorDC]

If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

A) 25/36

B) 125/216

C) 91/216

D) 11/36

E) 36/216

OA C

Source: Veritas Prep

[Ian Stewart]

There's a 5/6 chance we don't get a '3' on one roll, so a (5/6)^3 = 125/216 chance we don't get a '3' on any of our three rolls. So the probability we do get at least one '3' is 1 - (125/216) = 91/216.

[Scott@TargetTestPrep]

If a fair die is rolled three times, what is the probability that a 3 occurs on at least one roll?

A) 25/36

B) 125/216

C) 91/216

D) 11/36

E) 36/216

OA C

Source: Veritas Prep

We can use the following formula:

1 = P(at least one three) + P(no threes)

Let's determine P(no threes):

5/6 x 5/6 x 5/6 = 125/216

Thus, P(at least one three) = 1 - 125/216 = 91/216.

Answer: C