To find the theoretical probability that Talia lands on any letter in the word "Mississippi," we first need to analyze the letters in that word.
The word "Mississippi" has the following letters:
- M: 1 time
- I: 5 times
- S: 4 times
- P: 2 times
So the letters in "Mississippi" are M, I, S, and P, with counts as follows:
- Total unique letters = 4 (M, I, S, P)
- Total occurrences of letters in "Mississippi" = 11 (1 M + 5 I + 4 S + 2 P)
Now, since Talia is spinning a spinner with 26 equal spaces (labeled A to Z), the total possible outcomes are 26.
The favorable outcomes that correspond to the letters in "Mississippi" are M, I, S, and P, but we need to account for the fact that 'I' can show up 5 times, 'S' 4 times, and 'P' 2 times.
As we are interested in the letters that appear in the spinner, we only care about whether M, I, S, P appear at least once. Since all those letters are present in "Mississippi," we focus only on their unique occurrences.
The Formula for Theoretical Probability:
Theoretical probability is given by:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Number of Favorable Outcomes
The favorable outcomes are M, I, S, and P. There are 4 letters (considering their uniqueness) that can be landed on.
Total Number of Outcomes
The total outcomes from the spinner = 26.
Calculating the Probability:
The number of letters in "Mississippi" that correspond to the spinner is 4 (M, I, S, P).
So, we compute the probability as follows:
\[ P(\text{landing on M, I, S, or P}) = \frac{4}{26} = \frac{2}{13} \]
Final Answer:
Thus, the theoretical probability that Talia lands on any letter in the word "Mississippi" is:
Start Fraction 2 over 13 End Fraction