A letter is chosen from the word 'PENCIL', what is the probability that the letter chosen is a consonant?

Answer

To find the probability that the letter chosen from the word 'PENCIL' is a consonant, we can follow these steps:

### Step 1: Identify the total number of letters in the word 'PENCIL'.
The word 'PENCIL' consists of the letters: P, E, N, C, I, L.

**Total letters = 6**

### Step 2: Identify the consonants in the word.
The consonants in the word 'PENCIL' are:
- P (consonant)
- N (consonant)
- C (consonant)
- L (consonant)

The vowels in the word are:
- E (vowel)
- I (vowel)

**Total consonants = 4 (P, N, C, L)**

### Step 3: Calculate the probability of choosing a consonant.
The probability of an event is given by the formula:

\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case, the number of favorable outcomes (choosing a consonant) is 4, and the total number of outcomes (total letters) is 6.

\[ \text{Probability of choosing a consonant} = \frac{4}{6} \]

### Step 4: Simplify the fraction.
To simplify \(\frac{4}{6}\), we can divide both the numerator and the denominator by their greatest common divisor, which is 2.

\[ \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \]

### Final Answer:
The probability that the letter chosen is a consonant is \(\frac{2}{3}\).

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