Question

Suppose you roll a pair of six-sided dice.

What is the probability that the sum of the numbers on your dice is at least 9?

Answer 1

A pair of 6 sided dice is rolled.

So there are total of 36 possibilities.

The event is sum of the numbers on your dice is at least 9

Therefore sum can be 9,10,11 or 12

The possible pairs for

Sum as 9 : (4,5) , (5,4) , (6,3) , (3,6) so 4 pairs

Sum as 10: (4,6) , (5,5) , (6,4) so 3 pairs

Sum as 11: (5,6) , (6,5) so 2 pairs

Sum as 12: (6,6) so 1 pair

Therefore total of 1+2+3+4 = 10 pairs are there by which sum on dice is atleast 9

Hence the probability = 10/36 = 5/18