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 10.
the probability of rolling a number greater than 10 is
(type an integer or a simplified fraction.)

Explanation:

Step1: Identify favorable outcomes

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

Step2: Identify total outcomes

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

Step3: Calculate probability

Probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{n}{N}=\frac{2}{12}\). Simplify \(\frac{2}{12}\) by dividing numerator and denominator by 2, we get \(\frac{1}{6}\).

Answer:

\(\frac{1}{6}\)