Question
If Talia spins a spinner with 26 equal spaces (labeled A to Z) what is the theoretical probability that she lands on any letter in the word "Mississippi"?
a. 3/13
b. 2/13
c. 1/6
d. 2/3
a. 3/13
b. 2/13
c. 1/6
d. 2/3
Answers
GPT-4o mini
To find the theoretical probability that Talia lands on any letter in the word "Mississippi", we first identify the unique letters in that word and how many times each letter appears.
The letters in "Mississippi" are:
- M: 1 time
- I: 5 times
- S: 4 times
- P: 2 times
Now, we total the occurrences of these letters:
- Total occurrences of letters in "Mississippi" = 1 (M) + 5 (I) + 4 (S) + 2 (P) = 12
Now, since Talia spins a spinner with 26 equal spaces (labeled A to Z), the total number of possible outcomes is 26.
The probability is given by the formula:
\[
P(\text{landing on a letter in "Mississippi"}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{12}{26}
\]
Now, simplifying \( \frac{12}{26} \):
\[
\frac{12}{26} = \frac{6}{13}
\]
Since we're looking for the probability of landing on **any letter** in "Mississippi", we actually need to account for any letter that appears in the word, which includes M, I, S, and P. Thus, we see whether any of these letters contribute to meeting the expressed options.
However, in the response options provided (3/13, 2/13, 1/6, 2/3), none directly simplifies to our calculated probability of \( \frac{6}{13} \).
Please re-check the options for possible corrections or confirm any constraints on the probability choices, as the calculated answer of \( \frac{6}{13} = \frac{12}{26} \) accurately represents the theoretical probability based on the letter frequency in "Mississippi" and the total outcomes from the spinner.
The letters in "Mississippi" are:
- M: 1 time
- I: 5 times
- S: 4 times
- P: 2 times
Now, we total the occurrences of these letters:
- Total occurrences of letters in "Mississippi" = 1 (M) + 5 (I) + 4 (S) + 2 (P) = 12
Now, since Talia spins a spinner with 26 equal spaces (labeled A to Z), the total number of possible outcomes is 26.
The probability is given by the formula:
\[
P(\text{landing on a letter in "Mississippi"}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{12}{26}
\]
Now, simplifying \( \frac{12}{26} \):
\[
\frac{12}{26} = \frac{6}{13}
\]
Since we're looking for the probability of landing on **any letter** in "Mississippi", we actually need to account for any letter that appears in the word, which includes M, I, S, and P. Thus, we see whether any of these letters contribute to meeting the expressed options.
However, in the response options provided (3/13, 2/13, 1/6, 2/3), none directly simplifies to our calculated probability of \( \frac{6}{13} \).
Please re-check the options for possible corrections or confirm any constraints on the probability choices, as the calculated answer of \( \frac{6}{13} = \frac{12}{26} \) accurately represents the theoretical probability based on the letter frequency in "Mississippi" and the total outcomes from the spinner.