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 1. the probability of rolling a number greater than 1 is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the total number of outcomes

The total number of possible outcomes when rolling a 12 - sided die is \(n(S)=12\).

Step2: Determine the number of favorable outcomes

The numbers greater than 1 in the set \(\{1,2,3,4,5,6,7,8,9,10,11,12\}\) are \(2,3,4,5,6,7,8,9,10,11,12\). So the number of favorable outcomes \(n(E)=11\).

Step3: Use the probability formula

The probability formula is \(P(E)=\frac{n(E)}{n(S)}\). Substituting \(n(E) = 11\) and \(n(S)=12\), we get \(P(E)=\frac{11}{12}\).

Answer:

\(\frac{11}{12}\)