You roll two dice what is the probability that the sum of the dice is less than 5 and one dice shows a 2?

Lets say the 1st die rolled a 2 - there would be 2 combinations for which the sum of dice being < 5 : 2,1 2,2 Now say the 2nd die rolled a 2 - there would be 2 combinations for which the sum of dice being < 5 : 1,2 2,2 Now we want to count all cases where either dice showed a 2 and sum of the dice was < 5. However note above that the roll (2,2) is counted twice. So there are three unique dice roll combinations which answer the criteria of at least one die showing 2, and sum of dice < 5: 1,2 2,1 2,2 The total number of unique outcomes for two dice is 6*6=36 . So, the probability you are looking for is 3/36 = 1/12