A letter is picked at random from the letters of the work UNCOPYRIGHTABLE. Find the probability that it is a vowel.

Answer

To find the probability of picking a vowel from the letters of the word "UNCOPYRIGHTABLE," we will follow these steps:

### Step 1: Identify the total number of letters in the word.
The word "UNCOPYRIGHTABLE" consists of the following letters:
U, N, C, O, P, Y, R, I, G, H, T, A, B, L, E.

Counting these letters, we find:
- Total letters = 15.

### Step 2: Identify the vowels in the word.
The vowels in the English language are A, E, I, O, and U. Now, we will identify the vowels present in the word "UNCOPYRIGHTABLE":
- Vowels: U, O, I, A, E.

Counting these vowels, we find:
- Total vowels = 5.

### Step 3: Calculate the probability of picking a vowel.
The probability (P) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In our case:
- Number of favorable outcomes (vowels) = 5.
- Total number of outcomes (total letters) = 15.

So, the probability of picking a vowel is:
\[ P(\text{vowel}) = \frac{5}{15} \]

### Step 4: Simplify the fraction.
We can simplify the fraction:
\[ \frac{5}{15} = \frac{1}{3} \]

### Final Answer:
The probability that a letter picked at random from the word "UNCOPYRIGHTABLE" is a vowel is \( \frac{1}{3} \).

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