To find the theoretical probability that Tony will land on any letter in the word "Hippopotamus," we first need to determine how many unique letters are in the word.
The word "Hippopotamus" consists of the following letters:
- H
- I
- P
- O
- T
- A
- M
- U
- S
Now, let's count the unique letters:
- H
- I
- P
- O
- T
- A
- M
- U
- S
The letter "P" appears twice but counts only as one unique letter, and the letter "O" appears twice but counts only as one unique letter.
So, the unique letters in "Hippopotamus" are: H, I, P, O, T, A, M, U, S.
That gives us a total of 9 unique letters.
The total number of possible outcomes when spinning the spinner is 26 (one for each letter of the alphabet).
Thus, the theoretical probability \( P \) of landing on any letter from the word "Hippopotamus" is given by the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{9}{26} \]
Now we can check the provided response options:
- \( \frac{9269}{26} \) is not relevant here.
- \( \frac{6136}{13} \) simplifies to \( \frac{9}{26} \) (as \( \frac{6136}{13} = 472 \)).
- \( \frac{2132}{13} \) does not relate to our calculation.
- \( 161 \) sixth is also not relevant.
Since the equivalent of \( \frac{9}{26} \) was found in the \( 6136/13 \) option, we confirm that:
The theoretical probability of landing on any letter in "Hippopotamus" is \( \frac{6136}{13} \).