Sixteen cards are labelled as a, b, c,…… m, n. o,p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is :
(i) a vowel

Answer

To solve the problem of finding the probability that the card drawn is a vowel, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Cards**:
The total number of cards is given as 16. These cards are labeled from 'a' to 'p'.

**Hint**: Count the letters from 'a' to 'p' to confirm the total number of cards.

2. **List the Vowels**:
The vowels in the English alphabet are 'a', 'e', 'i', 'o'. We need to identify how many of these vowels are present in the set of cards.

**Hint**: Recall the vowels in the English alphabet and check which ones are included in the labels of the cards.

3. **Count the Number of Vowels**:
From the labels 'a', 'b', 'c', ..., 'p', the vowels are 'a', 'e', 'i', and 'o'. Thus, there are 4 vowels.

**Hint**: Make a list of the vowels found in the cards and count them.

4. **Calculate the Number of Favorable Outcomes**:
The number of favorable outcomes (drawing a vowel) is 4 (the vowels 'a', 'e', 'i', and 'o').

**Hint**: Favorable outcomes are the specific outcomes you are interested in, which in this case are the vowels.

5. **Calculate the Probability**:
The probability \( P \) of drawing a vowel is given by the formula:
\[ P(\text{vowel}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{4}{16} \]

**Hint**: Remember that probability is calculated as the ratio of favorable outcomes to total outcomes.

6. **Simplify the Probability**:
Simplifying \( \frac{4}{16} \) gives \( \frac{1}{4} \).

**Hint**: Simplification involves dividing both the numerator and denominator by their greatest common divisor.

### Final Answer:
The probability that the card drawn is a vowel is \( \frac{1}{4} \).