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 less than 6. the probability of rolling a number less than 6 is (type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of favorable outcomes

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

Step2: Determine the total number of outcomes

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

Step3: Calculate the probability

The probability formula is \(P=\frac{n}{N}\). Substituting \(n = 5\) and \(N = 12\), we get \(P=\frac{5}{12}\).

Answer:

\(\frac{5}{12}\)