# 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?

QUESTION POSTED AT 01/06/2020 - 03:09 PM

QUESTION POSTED AT 01/06/2020 - 03:09 PM

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.]

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.]

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