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 22. the probability of rolling a number less than 22 is \\(\square\\). (type an integer or a simplified fraction.)

Explanation:

Step1: Determine total outcomes

The die has 12 sides, so total outcomes \( n(S) = 12 \).

Step2: Determine favorable outcomes

All numbers on the die (\( 1,2,\dots,12 \)) are less than 22. So favorable outcomes \( n(E) = 12 \).

Step3: Calculate probability

Probability \( P(E) = \frac{n(E)}{n(S)} = \frac{12}{12} = 1 \).

Answer:

\( 1 \)