Question 1166681: You roll two six-sided dice. What is the probability that the sum will be odd or a multiple of three? Round your answer to the nearest tenth of a percent.
Answer by themasterofcircuits(27)   (Show Source):
You can put this solution on YOUR website! Let A be the sum is odd
Let B be the sum is a multiple of three
P(A or B)=P(A)+P(B)-P(A and B)
Possible odd sums: 3,5,7,9,11
3: (1,2) or (2,1)
5: (1,4), (4,1), (3,2), or (2,3)
7: (2,5), (5,2), (3,4), (4,3), (6,1), or (1,6)
9: (3,6), (6,3), (5,4), or (4,5)
11: (5,6),(6,5)
This could occur 18 times out of 36 dice roll possibilities.
So, P(A) =  or 0.5 or 50%
Possible multiples of 3:
3: (1,2) or (2,1)
6: (1,5), (5,1), (2,4), (4,2), (3,3)
9: (3,6), (6,3), (5,4), or (4,5)
12: (6,6)
This could occur 12 times out of 36 dice roll possibilities.
So, P(B) =  or 0.33 or 33%
Now, we need to find the possibilities they have in common. They are:
3: (1,2) or (2,1)
9: (3,6), (6,3), (5,4), or (4,5)
This could occur 6 times out of 36 dice roll possibilities.
So, P(A and B) =  or 0.166 or 16.6%
Since P(A or B)=P(A)+P(B)-P(A and B):
P(A or B) = +-=
Rounded to the nearest tenth of a percent: P(A or B) = 66.7%
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