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 \boxed{}. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the maximum sum of two dice rolls

The maximum number on a die is \(6\). When rolling two dice, the maximum sum is \(6 + 6=12\).

Step2: Compare the maximum sum with the given sum

Since \(12<15\), there are \(0\) outcomes where the sum of two dice - roll numbers exceeds \(15\).

Step3: Calculate the probability

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the number of all possible outcomes. Here, \(n(A) = 0\) and \(n(S)=36\). So \(P=\frac{0}{36}\).

Answer:

\(0\)