Question 509335: What is the probability of getting either a sum of 8 or at least one 6 in the roll of a pair of dice?
Found 2 solutions by swincher4391, Edwin McCravy:
Answer by swincher4391(1107)   (Show Source):
You can put this solution on YOUR website! How many possibilities are there on two 6 sided dice? 36.
How many possibilities give you at least a 6 on the dice? (1,6;2,6;3,6;4,6;5,6;6,6;6,1;6,2;6,3;6,4;6,5;) 11
How many possibilities give you a sum of 8? (2,6;3,5;4,4;5,3;6,2) 5
P(one 6 or sum of 8) = P(one 6) + P(sum of 8)=11/36 + 5/36 = 18/36 = 1/2 <--- Answer
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
The other tutor's answer is incorrect.
I have colored all the ones red that
either have a sum of 8 or that have
at least one 6.
⚀⚀ ⚀⚁ ⚀⚂ ⚀⚃ ⚀⚄ ⚀⚅
⚁⚀ ⚁⚁ ⚁⚂ ⚁⚃ ⚁⚄ ⚁⚅
⚂⚀ ⚂⚁ ⚂⚂ ⚂⚃ ⚂⚄ ⚂⚅
⚃⚀ ⚃⚁ ⚃⚂ ⚃⚃ ⚃⚄ ⚃⚅
⚄⚀ ⚄⚁ ⚄⚂ ⚄⚃ ⚄⚄ ⚄⚅
⚅⚀ ⚅⚁ ⚅⚂ ⚅⚃ ⚅⚄ ⚅⚅
Count the red ones. There are 14 of them.
Count all the rolls. There are 36 of them.
So the probability is 14 out of 36 or
 which reduces to  .
Edwin
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