Two dice are thrown simultaneously. Given that sum of the numbers is NOT more than 5, what is the probability that sum is more than 3? 7/10 3/10 5/6 3/4 9/10

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Two dice are thrown simultaneously. Given that sum of the numbers is NOT more than 5, what is the probability that sum is more than 3? 7/10 3/10 5/6 3/4 9/10

Mathematics
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we are given that the sum is NOT more than 5 so this is our sample space how many ways can you get a sum NOT more than 5 ?
the sum can be 2, 3, 4 or 5, yes ?

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Other answers:

yes
how many ways can you get a sum of 2 ?
one way?
yes, ``` sum = 2 (1 way) ```
what about the sum of 3, how many ways ?
one way??
you can have : 1 + 2 or 2 + 1 so two ways right
ohh right, i didn't think you could count both
ways
ok good, ``` sum = 2 (1 way) sum = 3 (2 way) ```
what about sum = 4, how many ways ?
3? 2+2, 3+1, 1+3
Very good : 1 + 3 = 4 2 + 2 = 4 3 + 1 = 4
so we have ``` sum = 2 (1 way) sum = 3 (2 way) sum = 4 (3 way) ```
can you guess how many ways there will be for getting a sum of 5 ?
4?
thats it, we're almost done ``` sum = 2 (1 way) sum = 3 (2 way) sum = 4 (3 way) sum = 5 (4 way) ```
so how many total ways are there for getting a sum NOT more than 5 ?
3 ways?
oh wait...4?
nope, just add them up : 1+2+3+4 = ?
10!
Yes! how many of them have sum more than 3 ?
6?
how ?
just look at the table that we have created earlier ``` sum = 2 (1 way) sum = 3 (2 way) sum = 4 (3 way) sum = 5 (4 way) ```
simply add the number of ways that we can get sum of 4 and 5
2?
how ?
im sorry! i suck
sum = 2 (1 way) sum = 3 (2 way) `sum = 4 (3 way)` `sum = 5 (4 way)` add them : 3+4 = 7 ways
outcomes in favor = 7 total outcomes = 10 probability = ?
right...im so stupid 7/10
you're not stupid, you're doing great! thest things takes practice
thank you! no wonder you have so many fans! haha
haha that is because i have been here so long yw :)

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