Consider the experiment of randomly selecting a number from 1 to 12 (Including 1 and 12). (a) What is the sample space of this experiment? $$ S=\{ $$ Enter your answer $$ \} $$ (Enter your answer as a comma-separated list.) (b) Calculate the probability of selecting a number greater than 11 . $$ \mathrm{P}= $$ Enter your answer (Enter your answer as a fraction.)

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(a) The sample space $$ S $$ consists of all integers from 1 to 12 (inclusive). Therefore,

$$
S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}
$$

(b) To find the probability $$ \mathrm{P} $$ of selecting a number greater than 11:

- **Total number of possible outcomes:** 12
- **Favorable outcomes (numbers greater than 11):** Only the number 12

Thus,

$$
\mathrm{P} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{12}
$$

**Answer:**

(a) $$ S = \{1,2,3,4,5,6,7,8,9,10,11,12\} $$

(b) $$ \mathrm{P} = \frac{1}{12} $$
(a) The sample space $$ S $$ is $$ \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\} $$. (b) The probability $$ \mathrm{P} $$ of selecting a number greater than 11 is $$ \frac{1}{12} $$.

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