Question
What is the theoretical probability of spinning letters C and E or E and C in the word clean
Answers
GPT-4o mini
To determine the theoretical probability of spinning the letters C and E or E and C in the word "clean," we first need to identify the total number of letters in the word and the favorable outcomes.
The word "clean" has the following letters: C, L, E, A, N. This totals 5 letters.
The favorable outcomes for the event of spinning "C and E" or "E and C" can be considered as the combinations of selecting these two letters. Let's outline the steps:
1. **Total possible outcomes**: When spinning, you have 5 letters (C, L, E, A, N), so there are 5 possible outcomes.
2. **Favorable outcomes**: The event of spinning "C and E" or "E and C" occurs when either of these combinations is selected. Let's consider these as follows:
- Getting the letters C and E: This involves two events (if we're considering multiple spins), but since you only spin once and can only get one letter per spin, C and E means you are looking for the probability of either occurring.
- Therefore, the favorable outcomes (either C or E) are simply C and E.
Now, counting favorable outcomes:
- There is 1 favorable outcome for C.
- There is 1 favorable outcome for E.
Thus, the total number of favorable outcomes for C or E is 2.
3. **Calculating the probability**:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{5}
\]
So, the theoretical probability of spinning either the letter C or the letter E from the word "clean" is \(\frac{2}{5}\).
The word "clean" has the following letters: C, L, E, A, N. This totals 5 letters.
The favorable outcomes for the event of spinning "C and E" or "E and C" can be considered as the combinations of selecting these two letters. Let's outline the steps:
1. **Total possible outcomes**: When spinning, you have 5 letters (C, L, E, A, N), so there are 5 possible outcomes.
2. **Favorable outcomes**: The event of spinning "C and E" or "E and C" occurs when either of these combinations is selected. Let's consider these as follows:
- Getting the letters C and E: This involves two events (if we're considering multiple spins), but since you only spin once and can only get one letter per spin, C and E means you are looking for the probability of either occurring.
- Therefore, the favorable outcomes (either C or E) are simply C and E.
Now, counting favorable outcomes:
- There is 1 favorable outcome for C.
- There is 1 favorable outcome for E.
Thus, the total number of favorable outcomes for C or E is 2.
3. **Calculating the probability**:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{5}
\]
So, the theoretical probability of spinning either the letter C or the letter E from the word "clean" is \(\frac{2}{5}\).