SOLUTION: Two dice are tossed. What is the probability that their sum will be 3, given that exactly one face shows 2? (Round your answer to three decimal places.)

Here are all rolls of the dice, the sample space,
which contains 36 elements:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6) 

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6) 

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)


Since we are given that exactly one face shows 2, we reduce
the sample space to contain only those rolls that have exactly
one face showing 2.  That is, we eliminate from the sample space
all the rolls that don't have exactly one face showing 2. So the 
reduced sample space has only 10 elements.  Count them. The ones 
that have sum 3 are colored red:

      (1,2) 

(2,1)       (2,3) (2,4) (2,5) (2,6)

      (3,2)  

      (4,2)  

      (5,2) 

      (6,2)

So the desired conditional probability is
2 out of 10 or  or 

Edwin