A letter is chosen at random from English alphabets. The probability of that letters pf the word CYLINDER is .

Options

A. `4//13`
B. `13//4`
C. `2//13`
D. `13//2`

Answer

To solve the problem of finding the probability of choosing a letter from the word "CYLINDER," we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Sample Space**:
The sample space consists of all the letters in the English alphabet. There are a total of 26 letters in the English alphabet.

**Hint**: Remember that the English alphabet consists of letters from A to Z.

2. **Identify the Unique Letters in "CYLINDER"**:
Next, we need to identify the unique letters in the word "CYLINDER". The letters are C, Y, L, I, N, D, E, R.

**Hint**: Count each letter only once, even if it appears multiple times in the word.

3. **Count the Unique Letters**:
The unique letters in "CYLINDER" are C, Y, L, I, N, D, E, R, which gives us a total of 8 unique letters.

**Hint**: List out the letters to ensure you count them correctly.

4. **Calculate the Probability**:
The probability of choosing a letter from "CYLINDER" when a letter is chosen at random from the English alphabet can be calculated using the formula:

\[ P(E) = \frac{N(E)}{N(S)} \]

where \(N(E)\) is the number of favorable outcomes (unique letters in "CYLINDER") and \(N(S)\) is the total number of outcomes (total letters in the English alphabet).

Here, \(N(E) = 8\) and \(N(S) = 26\).

So, the probability \(P(E)\) is:

\[ P(E) = \frac{8}{26} \]

5. **Simplify the Probability**:
We can simplify \(\frac{8}{26}\) by dividing both the numerator and the denominator by 2:

\[ P(E) = \frac{4}{13} \]

### Final Answer:
The probability of choosing a letter from the word "CYLINDER" is \(\frac{4}{13}\).

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