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 15.
the probability of getting two numbers whose sum exceeds 15 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 \(6\). The sum of two dice rolls is \(S = a + b\) (where \(a\) is the result of the first roll and \(b\) is the result of the second roll). The maximum value of \(S\) is \(6 + 6=12\).

Step2: Analyze the condition for the sum exceeding 15

Since the maximum sum of two dice rolls \(S_{max}=12\), and \(12<15\), there are \(n = 0\) outcomes where the sum of the two - rolled numbers exceeds 15. The total number of possible outcomes \(N = 36\).

Using the probability formula \(P=\frac{n}{N}\), we substitute \(n = 0\) and \(N = 36\) into the formula.

Answer:

\(0\)