Which is more likely rolling a total of 9 when two dice are

Which is more likely: rolling a total of 9 when two dice are rolled or rolling a total of 9 when three dice are rolled?

Solution

Answer :

First we have to determine the probability of two die summing to 9. I began by calculating the sample space. There are 6 * 6 different ways the two die could sum. Now to figure out how many of those ways sum to 9.

The favourable out comes are ( 3 , 6 ) , ( 6, 3 ) , ( 5 , 4 ) , ( 4 , 5 )

So the probability of rolling two dice which sum to 9 is 4/6² = 4/36 =1/9

, while rolling a 9 with three dice has the probability is [ 8C₂ – 3]/6³ = 25/216 which is greater

Computing the probabilities I found that 25/216 > 1/9 .

Therefore , Therefore, it is more likely with 3 dice.