A dice is rolled twice. What is the probability that the number in the second roll will be higher than that in the first?
The number in the second roll can be either same, or lower or higher than that in the first.
There is 1 out of 6 probability that the two rolls will be the same, hence a 5 out of 6 probability that they will be different. Moreover, the probability that the first roll is greater than the second must be equal to the probability that the second roll is greater than the first, so both probabilities must be 2.5 out of 6 or 5 out of 12 or 15 out of 36.
The number of total possibilities when two dice are rolled is 36. The question is similar to count the number of ordered pairs where the second co-ordinate is less than the first co-ordinate. The number of pairs will be 0+1+2+3+4+5 = 15.
The correct option is C.