The letters of the word mississippi are put in a bowl, what is the probability you will pick a vowel, replace it in the bowl, and then pick a P

To solve this problem, let's break it down step by step.

1. **Identify the total number of letters**:  
   The word "mississippi" has 11 letters.

2. **Identify the vowels and their frequency**:  
   The vowels in "mississippi" are **i** and **i** (since we only count distinct vowels). The letter "i" appears 4 times in the word.

3. **Calculate the probability of picking a vowel**:  
   There are 4 vowels (all 'i's) out of 11 letters.  
   So, the probability of picking a vowel (i.e., an "i") is:

   \[
   P(\text{vowel}) = \frac{4}{11}
   \]

4. **Identify the frequency of the letter 'P'**:  
   The letter "P" appears 2 times in the word.

5. **Calculate the probability of picking a 'P' after replacing the vowel**:  
   Since the letter is replaced back into the bowl, the total number of letters remains 11.  
   The probability of picking a 'P' is:

   \[
   P(\text{P}) = \frac{2}{11}
   \]

6. **Calculate the combined probability**:  
   The events are independent (since the letter is replaced), so the combined probability is:

   \[
   P(\text{vowel, then P}) = P(\text{vowel}) \times P(\text{P}) = \frac{4}{11} \times \frac{2}{11} = \frac{8}{121}
   \]

Therefore, the probability that you will pick a vowel, replace it, and then pick a 'P' is \(\frac{8}{121}\).

Would you like more details on any of the steps? Here are some related questions:

1. How do you calculate the probability of picking a consonant instead of a vowel?
2. What would the probability be if the letter was not replaced after the first draw?
3. How does the probability change if there were more letters added to the word?
4. Can this method be used for any word? What changes would be necessary?
5. What is the total probability of picking two consonants in two draws, with replacement?

**Tip:** Always check if the problem involves replacement or not, as this significantly affects the calculation of probabilities.

Explore the probability of picking a vowel followed by the letter 'P' from the word 'mississippi'. Understand step-by-step calculations involving replacement and independence. Suitable for Grades 7-9 students and anyone interested in basic probability problems.

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