Question

a pair of dice is rolled. what is the probability of getting a sum of 4? what is the probability of getting a sum of 4? (simplify your answer. type a fraction.)

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:

\(\frac{1}{12}\)