If a single letter is selected at random from the word "PROBABILITY", then the probability that it is a vowel is

Options

A. `(1)/(3)`
B. `(4)/(11)`
C. `(2)/(11)`
D. `(3)/(11)`

Explanation

To find the probability that a randomly selected letter from the word "PROBABILITY" is a vowel, we can follow these steps:

### Step 1: Identify the total number of letters in the word "PROBABILITY".
The word "PROBABILITY" consists of the following letters: P, R, O, B, A, B, I, L, I, T, Y.

**Total letters = 11**

### Step 2: Identify the vowels in the word.
The vowels in the English alphabet are A, E, I, O, and U.

In the word "PROBABILITY", the vowels are:
- O
- A
- I (appears twice)

**Total vowels = 4 (O, A, I, I)**

### Step 3: Calculate the probability of selecting a vowel.
The probability (P) of an event is given by the formula:

\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

Here, the number of favorable outcomes (vowels) is 4, and the total number of outcomes (letters) is 11.

So, the probability of selecting a vowel is:

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

### Final Answer:
The probability that a randomly selected letter from the word "PROBABILITY" is a vowel is \( \frac{4}{11} \).

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