A letter is chosen at random from the word ASSASSINATION. Find the probability that letter is (i) a vowel (ii) a consonant.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Identify the total number of letters in the word "ASSASSINATION".

The word "ASSASSINATION" consists of the following letters:
A, S, S, A, S, S, I, N, A, T, I, O, N

Counting these letters, we find that there are a total of 13 letters.

**Total letters = 13**

### Step 2: Identify the vowels in the word.

The vowels in the English alphabet are A, E, I, O, U. Now, we will count the vowels in the word "ASSASSINATION":
- A appears 3 times
- I appears 2 times
- O appears 1 time

Adding these, we find the total number of vowels:
**Total vowels = 3 (A) + 2 (I) + 1 (O) = 6**

### Step 3: Calculate the probability of choosing a vowel.

The probability of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

For vowels:
\[ P(\text{vowel}) = \frac{\text{Total vowels}}{\text{Total letters}} = \frac{6}{13} \]

### Step 4: Identify the consonants in the word.

Now, we will count the consonants in the word "ASSASSINATION":
- S appears 5 times
- N appears 2 times
- T appears 1 time

Adding these, we find the total number of consonants:
**Total consonants = 5 (S) + 2 (N) + 1 (T) = 8**

### Step 5: Calculate the probability of choosing a consonant.

Using the same probability formula:
\[ P(\text{consonant}) = \frac{\text{Total consonants}}{\text{Total letters}} = \frac{8}{13} \]

### Final Answers:
(i) The probability that the letter chosen is a vowel is \( \frac{6}{13} \).

(ii) The probability that the letter chosen is a consonant is \( \frac{8}{13} \).

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