A letter of English alphabet is chosen at random. What is the probability that it is a letter of the word 'MATHEMATICS'?

Answer

To solve the problem of finding the probability that a randomly chosen letter from the English alphabet is a letter from the word "MATHEMATICS", we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Letters in the English Alphabet**:
- The English alphabet consists of 26 letters.

2. **Identify the Unique Letters in the Word "MATHEMATICS"**:
- The letters in "MATHEMATICS" are: M, A, T, H, E, M, A, T, I, C, S.
- To find the unique letters, we list them without repetition: M, A, T, H, E, I, C, S.
- Thus, the unique letters are: M, A, T, H, E, I, C, S (total of 8 unique letters).

3. **Calculate the Probability**:
- The probability \( P \) of selecting a letter from the word "MATHEMATICS" can be calculated using the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Here, the number of favorable outcomes (unique letters from "MATHEMATICS") is 8, and the total number of outcomes (letters in the English alphabet) is 26.
- Therefore, the probability is:
\[ P = \frac{8}{26} \]

4. **Simplify the Probability**:
- To simplify \( \frac{8}{26} \), we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
\[ P = \frac{8 \div 2}{26 \div 2} = \frac{4}{13} \]

### Final Answer:
The probability that a randomly chosen letter is from the word "MATHEMATICS" is \( \frac{4}{13} \).

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