What is the probability that the total of two dice will be greater than 7, given that the first die is a 5?

We are given that the first die shows up 5 and the total of the
dice is greater than 7.

Now we need to use conditional probability
here. We have to determine the probability of the total being greater than 7 given that the first
die is 5.

Let A denote the event that the first die is
5.

Let B denote the set that the sum of the dice is greater than 7
and the first die has a 5. Now B includes the following values of the dice, (5 , 3), (5 , 4), (5,
5) and ( 5, 6)

The possibility of getting a 5 when the first die is
thrown is (1/6). So P(A) = 1/6.

The possibility of getting the 4
options that constitute the set B is 4/ 36 = 1/9

Therefore P( B|A) =
P( A and B) / P(A) = (1/9) / (1/6)

= 6/
9

= 2/3

Therefore the
required probability is 2/3.