Question

A fair dice is rolled 4 times. What is the probability that at least 2 of the numbers are the same? Use the format a/b.

Answer 1

This is one minus the probability that none of the numbers are the same. If you roll the dice 4 times and all the numbers must be different then for the first throw there are 6 possible numbers, for the next 5, then there are 4 left, and finally you have 3 possible numbers, so there are:

6*5*4*3 possible dice throws such that each of the four yields a different number. The probability of this happening is thus:

6*5*4*3/6^4 = 5*4*3/6^3 = 5/18

So, the probability that 2 or more are the same is 1-5/18 = 13/18