SOLUTION: you roll 2 dice. whats the probability that the sum of the dice is even or the sum of the dice is less than 6?

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Question 316511: you roll 2 dice. whats the probability that the sum of the dice is even or the sum of the dice is less than 6?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
When you roll 2 dice, there are 36 possible outcomes.
Half sum to even, half sum to odd.
P(even sum)=18/36
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Ten outcomes sum to less than 6.
(1,1)(1,2)(1,3)(1,4)=+highlight%28+2%29,3,highlight%284%29,5
(2,1)(2,2)(2,3)=3,highlight%284%29,5
(3,1)(3,2)=highlight%284%29,5
(4,1)=5
P(sum < 6)=10/36
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From the total, we have to take out sum that are even and less than six or we would double count those.
There are 4 of those (highlighted in red).
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P(even sum or sum<6)=18/36+10/36-4/36=24/36=2/3