Two Fair die are rolled. What is the probability of one of the dice showing 5 or the sum being at least 8?

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Two Fair die are rolled. What is the probability of one of the dice showing 5 or the sum being at least 8?

Mathematics
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write down the cases in which the sum can be 8 with one of them being 5
okay should I include (5,3) and (3,5)
or no repeats

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you include both
okay I did that
arent you getting the answer?
it says a sum of at least 8
oops yeah so inluse(5,4) (4,5), (5,5) (5,6)(6,5)
okay I did that and there are a total 15 ways to make a sum of at least 8
"okay I did that and there are a total 15 ways to make a sum of at least 8" That is correct. It is necessary to avoid double counting, therefore the next step is to find out how many occurrences of 5 there are on one of the dice where the sum of the numbers on the pair is less than 8.
There are two, but does (5,5) count or no because its on two die?
There are more than two. Also (5, 5) does not count because it is already in the total of the 15 ways to make at least 8.
are there four?
Yes, four: (2, 5) (1, 5) (5,2) (5,1).
okay, so now what?
So the total number of ways to get one of the dice showing 5 or the sum being at least 8 (without double counting) is 15 + 4 = 19 ways. What is the value of the sample space?
what do you mean the value of the sample space?
The sample space has 36 possible combinations of numbers.
oh okay. Now i know what you mean
so its 19/36?
Yes, you are correct.
OMG thank you so much, I've been stuck on that problem for over an hour :D. You are a lifesaver xD
You're welcome :)

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