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
