Two dice are rolled and someone indicates that the two numbers that come up are different. Find the probability that the sum of the two numbers is 8.

Answer: 5/36

Step-by-step explanation:

We assume it's a fair die and the probability of any number coming up is 1/6.

Let's denote first die with it's number as A2, that is first die roled number 2

Let's denote second die with it's number as B4, that is Second die rolled 4.

For us to have the sum of those numbers to be 8, then we have possibilities of rolling the numbers

A2 and B6, A3 and B5, A4 and B4, A5 and B3, A6 and B2

This becomes:

[pr (A2) * pr (B6) ] + [pr (A3) * pr (AB5) ] + [pr (A4) * pr (B4) ] + [pr (A5) * pr (3) ] + [pr (A6) * pr (B2) ]

Which becomes:

[1/6 * 1/6] + [1/6 * 1/6] + [1/6 * 1/6] + [1/6 * 1/6 + [1/6 * 1/6]

Which becomes:

1/36 + 1/36 + 1/36 + 1/36 + 1/36 = 5/36

Hence, the probability of the sum of the two numbers on the dice being 8 is 5/36