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: Determine the total number of outcomes

The total number of equally - likely outcomes when a die is rolled twice is \(n(S)=36\) (as given in the problem).

Step2: Find the number of favorable outcomes

Let the first roll result be \(x\) and the second roll result be \(y\). We want \(x + y=3\). The possible pairs \((x,y)\) are \((1,2)\) and \((2,1)\). So \(n(A)=2\).

Step3: Calculate the probability

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\). Substituting \(n(A) = 2\) and \(n(S)=36\), we get \(P(A)=\frac{2}{36}\). Simplifying \(\frac{2}{36}=\frac{1}{18}\) (dividing numerator and denominator by 2).

Answer:

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