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 exceeds 13.
the probability of getting two numbers whose sum exceeds 13 is □
(type an integer or a simplified fraction.)

Explanation:

Step1: Determine the maximum sum of two dice rolls

The maximum number on a die is \(6\). So the maximum sum of two dice rolls is \(6 + 6=12\).

Step2: Calculate the probability

Since the maximum sum of two dice rolls is \(12\), and \(12<13\), the number of outcomes where the sum of two numbers exceeds \(13\) is \(n = 0\).
The formula for probability is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of elements in the event \(A\) and \(n(S)\) is the number of elements in the sample space. Here, \(n(S) = 36\). So \(P=\frac{0}{36}\).

Answer:

\(0\)