Question 1122548: Two fair six-sided dice are rolled.
What is the probability the sum of the numbers on the two dice is 5?
What is the probability the sum is 6?
What is the probability the sum is not 4?
What is the probability the sum is either 8 or 10?
What is the probability the sum is neither 9 nor 7?
Enter your answers as fractions in lowest terms.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! There are 36(6^2) possible events in the sample space, they are
:
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
:
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
:
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
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(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
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(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
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(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
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Probability(P) that the sum is 5, the following events satisfy this criteria
:
(1,4), (2,3), (3,2), (4,1)
:
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P that the sum is 5 = 4/36 = 1/9
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:
P that the sum is six
:
(1,5), (2,4), (3,3), (4,2), (5,1)
:
***************************************
P that the sum is six = 5/36
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P the sum is not four, first list the sums that are 4
:
(1,3), (2,2), (3,1)
:
*************************************************
P that the sum is not 4 = 1 -3/36 = 33/36 = 11/12
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P that the sum is 8 or 10
:
(2,6), (3,5), (4,4), (5,3), (6,2), (4,6), (5,5), (6,4)
:
****************************************************
P that the sum is 8 or 10 = 8/36 = 2/9
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P that the sum is neither 9 nor 7, first list the sums that are 9 or 7
:
(3,6), (4,5), (5,4), (6,3), (1,6), (2,5), (3,4), (4,3), (5,2), (6,3)
:
************************************************************
P that the sum is neither 9 nor 7 = 1 -10/36 = 26/36 = 13/18
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