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

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by Ian Stewart » Thu Jul 18, 2019 6:36 am
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.
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by Scott@TargetTestPrep » Mon Jul 29, 2019 3:20 pm
BTGmoderatorDC wrote: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

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