Question

a 12 - sided die is rolled. the set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12}. find the probability of rolling a number greater than 13. the probability of rolling a number greater than 13 is \\(\square\\). (type an integer or a simplified fraction.)

Explanation:

Step1: Determine total outcomes

A 12 - sided die has 12 possible outcomes, so total number of outcomes \(n(S)=12\).

Step2: Determine favorable outcomes

We need to find the number of outcomes where the number rolled is greater than 13. Looking at the set \(\{1,2,3,4,5,6,7,8,9,10,11,12\}\), there are no numbers greater than 13. So the number of favorable outcomes \(n(A) = 0\).

Step3: Calculate probability

The formula for probability is \(P(A)=\frac{n(A)}{n(S)}\). Substituting \(n(A) = 0\) and \(n(S)=12\), we get \(P(A)=\frac{0}{12}=0\).

Answer:

\(0\)