Jar A contains the 8 letters in the word Colorado. Jar B contains the 11 letters in the word Connecticut. What is the probability of randomly drawing two vowels from Jar A without replacing the first?
To find the probability, we need to find the total number of outcomes and the number of favorable outcomes.
The word "Colorado" has 4 vowels (o, o, a, o).
The total number of outcomes of drawing 2 letters without replacement from Jar A is C(8, 2) = 8! / (2! * (8-2)!) = 28.
The number of favorable outcomes is the number of ways to choose 2 vowels from the 4 vowels in Jar A. This is C(4, 2) = 4! / (2! * (4-2)!) = 6.
So, the probability of randomly drawing two vowels from Jar A without replacing the first is 6/28 = 3/14.
To find the probability of randomly drawing two vowels from Jar A without replacing the first, we will first determine the number of vowels in Jar A, which contains the word "Colorado."
1. Determine the number of vowels in "Colorado":
- There are three vowels in the word "Colorado" - 'o', 'o', and 'a'.
2. Determine the total number of letters in Jar A:
- Jar A contains 8 letters - 'C', 'o', 'l', 'o', 'r', 'a', 'd', 'o'.
3. Calculate the probability of drawing a vowel from Jar A for the first draw:
- The probability of drawing a vowel on the first draw is 3 vowels out of 8 total letters, which gives us a probability of 3/8.
4. Calculate the probability of drawing a vowel from Jar A for the second draw without replacement:
- After the first vowel is drawn, there are now 2 vowels remaining out of the total 7 letters (since one letter has already been drawn). Thus, the probability of drawing a vowel on the second draw is 2/7.
5. Calculate the overall probability of drawing two vowels without replacement:
- To calculate the overall probability, multiply the probabilities of the separate events, i.e., multiply the probability of drawing a vowel on the first draw (3/8) by the probability of drawing a vowel on the second draw (2/7): (3/8) * (2/7) = 6/56.
6. Simplify the resulting fraction:
- The fraction 6/56 can be simplified. Both 6 and 56 can be divided by 2: 6/56 = (6 ÷ 2) / (56 ÷ 2) = 3/28.
Therefore, the probability of randomly drawing two vowels from Jar A without replacing the first is 3/28.