An ordinary (fair) die is a cube with the numbers 1 through 6 ion the sides. imagine that such a die rolled twice in succession and that the face values are added together. the sum is recorded as the outcome of single trial of a random experiment. compute the probability if the sum is greater than 7

The probability would be 5/12.

When the sample space is written out we see that there are exactly 15 ways to have a sum greater than 7 on the two dice:  2 and 6; 3 and 5; 3 and 6; 4 and 4; 4 and 5; 4 and 6; 5 and 3; 5 and 4; 5 and 5; 5 and 6; 6 and 2; 6 and 3; 6 and 4; 6 and 5; 6 and 6.
 
There are a total of 36 entries in the sample space for this experiment.  15/36 = 5/12.

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