Given, Two fair six-sided dice are rolled. Each die has faces numbered 1 through 6 . Total number of outcomes: Since each die has 6 faces, the sample space size is N=6×6=36. Favourable outcomes (sum >7 ): We list all ordered pairs ( (i,j) ) with ( i+j>7 ): Sum =8:(2,6),(3,5),(4,4),(5,3),(6,2)⟶5 outcomes Sum =9:(3,6),(4,5),(5,4),(6,3)⟶4 outcomes Sum =10:(4,6),(5,5),(6,4)⟶3 outcomes Sum =11:(5,6),(6,5)⟶2 outcomes Sum =12:(6,6)⟶1 outcome Total favourable outcomes =(5+4+3+2+1=15).
Probability calculation: The probability that the sum is strictly greater than 7 is P(‌ sum ‌>7)=‌