Problem Solving

A pair of standard 6-sided dice is rolled. What is the probability that the sum of
the two dice is equal to 8?
A) 1/9
B) 1/8
C) 5/36
D) 1/6
E) 7/36

OA - C). Why is it not D?

Essentially, the number of ways one can get '8' = (2,6); (3,5) ;(4,4) ; (4,4); (5,3) and (6,2)

Why did I chose (4,4) two times? In the denominator, we have accounted for (4,4) two times because of fundamental principle of counting.

Please help .....

Thanks

No. In the denominator you have not counted (4,4) two times.

Have a look at this.

if the first dice is 1 then the second dice can be any of {1,2,3,4,5,6}.
so your pairs will be (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)

Now similarly if the first dice shows up 2 then the second dice can show up any of {1,2,3,4,5,6}.
so your pairs will be (2,1)(2,2)(2,3)(2,4)(2,5)(2,6)

Similarly write down all the possibilites and you wont get (4,4) counted twice.

Does this explain your question?

Can anyone explain little more detail of the above problem since I am stuck with this Quant question?

Thanks,
Pavan

possible options that will sum up to 8 are:
2,6 prob of 2 is 1/6 same for 6 so there joint probability is 1/6*1/6=1/36
3,5 1/36 for reason mentioned above
4,4 1/36 for reason mentioned above
5,3 1/36 for reason mentioned above
6,6 1/36 for reason mentioned above

so the sum is 5/36