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 11
the probability of rolling a number less than 11 is
(type an integer or a simplified fraction.)

Explanation:

Step1: Determine the number of favorable outcomes

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

Step2: Determine the total number of outcomes

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

Step3: Calculate the probability

The probability formula is \(P=\frac{n(F)}{n(T)}\). Substituting the values, we get \(P = \frac{10}{12}\). Simplifying the fraction (dividing numerator and denominator by 2), we have \(P=\frac{5}{6}\).

Answer:

\(\frac{5}{6}\)