A pair of dice is rolled 3 times. What is the probability that a sum of 8 on the 2 dice will occur at least once?

There are 36 outcomes when rolling a pair of dice.

The ones adding up to 8 are: (2,6), (3,5), (4,4), (5,3), (6,2).

So the probability of rolling a sum of 8 is 5/36.

With three (independent) random throws, the probability of having a sum of 8 at least once equals 1-probability of no 8 at all.

P (not 8) = 1-5/36=31/36

For this to happen three times, we use the multiplication rule

P (not 8 three times) = (31/36) ^3=29791/46656=

Therefore

P (sum of 8 at least once) = 1-29791/46656=16865/46656

[=0.3615 approx.]