Question

Two regular dice are rolled, find the probability that the sum is less than 13.

Answer 1

When 2 dice are thrown outcomes are,
S={(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)
      (4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
      (5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
      (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)}

Therefore total number of outcomes is 36.

Hence,  probability that the sum is less than 13 = 36/36 =1
Probability is 1 because sum of number appearing is always less than 13.