What is the probability that the sum of two rolled dice is 9 given that at least one of the dice rolled is a 4? Give your answer exactly as a fraction.

Answer 1

Let's assume that the dice are d6 (six sided dice) These have values from 1-6. There are 6*6 possible combos from two six sided dice, or 36 possibilities. If one die A is a 4, in order for the sum to be exactly 9, die B has to land on 5. Alternatively, if die B is the one that lands on 4, then die A has to land on 5. So, there are only 2 combos that sum to 9 and have at least 1 of the die be a 4. So the probability is:

(number of combos we want)/(total number of combos) = 2/36. Reduced, this is 1/18.