SOLUTION: Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The red one is 2, given that the sum is 7.

When two dice are rolling, the total space of events has 36 elements. 
These elements are the pairs (red,green),  where "red" and "green" are integer numbers from 1 to 6 inclusive.


These 36 elements of the space of events have equal probability of    each.


Of these 36 elements, exactly 6 (six) have the sum of 7:


    red     green

     1        6

     2        5

     3        4

     4        3

     5        2

     6        1


and only one pair  (red,green) = (2,5)  is favorable.


Therefore, the answer to the problem's question is 


    probability  P  =  = .    ANSWER




I made this simple calculation using the full space of events.



But you can easily get the same answer using the REDUCED space of events.

It consists of 6 listed elements, and only one of them is favorable;  so


    P = ,   


giving the same answer.