When rolling two fair 6 sided dice, what is the probability that the difference between the scores is more than 3?

Step-by-step explanation:

When we say, the difference of scores should be more than 3 it means that the difference can be 4 or 5.

Case 1: The difference of scores is 4.

The possible outcomes can be i.e. 4 number of cases are possible.

Case 2: The difference of scores is 5.

The possible outcomes can be . i.e. 2 number of cases.

Here, total number of favorable cases are 4 + 2 = 6.

Total number of cases, when two fair dice are rolled, are 36.

These cases are:

Formula:

Hence, the probability that the difference of scores is more than 3, at the roll of 2 dice, is i.e. .

Hence, the required probability is .