Question

a single die is rolled twice. the 36 equally - likely outcomes are shown to the right.
find the probability of getting two numbers whose sum is 3.
the probability of getting two numbers whose sum is 3 is
(type an integer or a simplified fraction.)

Explanation:

Step1: Identify favorable outcomes

We need to find the pairs \((x,y)\) where \(x + y=3\) and \(x,y\in\{1,2,3,4,5,6\}\). The possible pairs are \((1,2)\) and \((2,1)\). So there are 2 favorable outcomes.

Step2: Calculate total outcomes

The total number of outcomes when a die is rolled twice is \(6\times6 = 36\) (since each roll has 6 possibilities).

Step3: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{2}{36}=\frac{1}{18}\).

Answer:

\(\frac{1}{18}\)