a pair of dice is rolled. what is the probability of getting a sum of 4? what is the probability of getting…

Explanation:

Step1: Find total number of outcomes

When a pair of dice is rolled, each die has 6 possible outcomes. So the total number of outcomes when two dice are rolled is (6\times6 = 36) (by the fundamental counting principle).

Step2: Find number of favorable outcomes

The possible combinations to get a sum of 4 are ((1,3)), ((2,2)), ((3,1)). So there are 3 favorable outcomes.

Step3: Calculate probability

The probability (P) of an event is given by the formula (P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}). So (P=\frac{3}{36}=\frac{1}{12}).

Answer:

(\frac{1}{12})