To determine the sample space for this experiment, we need to list all the possible outcomes of choosing a random letter from the word "MATHEMATICS."

In probability, the sample space consists of all distinct outcomes. Since the experiment involves randomly choosing one letter, the sample space includes each unique letter in "MATHEMATICS." Duplicate letters are counted only once.

Analysis:

• The letters in "MATHEMATICS" are:
  M, A, T, H, E, M, A, T, I, C, S
  (Notice that some letters repeat: M appears twice, A appears twice, and T appears twice.)

• The distinct letters are:
  M, A, T, H, E, I, C, S.

Thus, the sample space is:
$\{ M, A, T, H, E, I, C, S \}.$

Correct Answer:

$\{ M, A, T, H, E, I, C, S \}.$

Would you like an explanation of why duplicates are excluded from the sample space? Let me know!

5 Related Questions:

1. How would the sample space change if each letter's frequency mattered?
2. What is the probability of selecting the letter "M" from the word "MATHEMATICS"?
3. How many total outcomes exist if duplicates are included in the sample space?
4. If vowels and consonants are grouped separately, what are the subsets of the sample space?
5. What is the total number of unique letters in the English alphabet, and how does it relate to this problem?

Tip:

In probability, when constructing a sample space, always list distinct outcomes to avoid over-counting.