Final answer:
The probability of rolling a sum of 4 on a standard pair of six-sided dice is 1/12, as there are 3 favorable outcomes out of a total of 36 possible outcomes.
Step-by-step explanation:
The probability of rolling a sum of 4 on a pair of six-sided dice involves determining all the possible combinations of two dice that add up to 4. The options are (1,3), (2,2), and (3,1). Each die has 6 sides, so there are a total of 6 x 6 = 36 possible outcomes when rolling two dice. Since there are 3 favorable outcomes that result in a sum of 4, the probability is therefore 3 out of 36. To express this in simplest fractional form, we divide both the numerator and the denominator by their greatest common divisor, which is 3, resulting in the probability of 1/12.
The mathematical expression for this probability is P(sum of 4) = 3/36 = 1/12.