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 less than 16. the probability of getting two numbers whose sum is less than 16 is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine total number of outcomes

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

Step2: Determine number of favorable outcomes

The maximum sum of two numbers when rolling a die twice is \(6 + 6=12\). Since \(12<16\), all \(36\) outcomes are favorable. Let \(n(E)\) be the number of favorable outcomes. So \(n(E) = 36\).

Step3: Calculate the probability

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting \(n(E) = 36\) and \(n(S)=36\), we get \(P(E)=\frac{36}{36}\).

Answer:

\(1\)