To find the theoretical probability that Talia lands on any letter in the word "Mississippi," let's first identify the unique letters in that word and their respective frequencies.
The word "Mississippi" has the following letters:
- M: 1
- I: 5
- S: 4
- P: 2
Now, we will count the total number of letters:
- Total letters in "Mississippi" = 11
Next, we need to count how many of these letters correspond to spaces on the spinner. Since the spinner has 26 equal spaces labeled from A to Z, we can say that there are no letters like that are outside of the English alphabet in our scenario.
Next, we count how many unique letters appear in "Mississippi":
- The letters M, I, S, and P are the unique ones.
From the spinner's 26 letters (A to Z), we need to determine how many of those are in "Mississippi":
- Relevant letters from the spinner that are in "Mississippi": M, I, S, P
- Total unique relevant letters (M, I, S, P) = 4
Now, let's find the total number of spaces in the spinner:
- Total spaces on the spinner = 26
The theoretical probability \( P \) that she lands on any letter in the word "Mississippi" is calculated by dividing the number of favorable outcomes (the 4 relevant letters) by the total number of outcomes (the 26 spaces):
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{26} = \frac{2}{13} \]
So, the theoretical probability that Talia lands on any letter in the word "Mississippi" is \( \frac{2}{13} \).
Thus, the answer is \( \frac{2}{13} \).