Question

Two dice are rolled one after the other. Find the probability that the sum of the dots on the dice total is a number greater than 11 if the second die is a 5.

Answer 1

Two dice are rolled one after the other.

Find the probability that the sum of the dots on the dice total is a number greater than 11,if the second die is a 5.

P(sum of the dots on the dice is greater 11/second die is a 5)

=P(sum of the dots is greater than 11 and second die is a 5)/P(second die is a 5)

Now , the denominator

=P(second die is a 5)

=1/6

And the numerator

=P(sum of the dots is greater than 11 and the second die is a 5)

=P(sum of the dots is 12 and the second die is a 5)

This is because the maximum sum of the dots is 6+6 = 12

=P( second dot is 5 and the first dot is 7)

=0

as a die can never show 7.

So,the required probability is 0.

Evidently,this is the mathematical proof.It is otherwise clear from the beginning that if the second die is a 5,then the sum of the dots can never be greater than 11,as in that case the first die would have to show a 7,which is not possible.

So,the required probability is 0.