On a particular day, at a crossing in a city, the various types of 280 vehicles going past during a time interval were observed as under:
`|{:("Type of vehicle","Two wheelers","Three wheelers","Four wheelers"),("Frequency"," 91"," 63"," 126"):}|`
Out of these vechicles , one is chosen at random, what is the probability that the chosen vechicle is
(i) a four wheeler
(ii) a two wheeler
(iii) a three wheeler?

Answer

To solve the given problem, we will calculate the probability of selecting a vehicle of each type (four wheeler, two wheeler, and three wheeler) from the total number of vehicles observed.

### Step-by-Step Solution:

1. **Identify the total number of vehicles:**
The total number of vehicles observed is given as 280.

2. **Identify the number of each type of vehicle:**
- Number of Two Wheelers = 91
- Number of Three Wheelers = 63
- Number of Four Wheelers = 126

3. **Calculate the probability of selecting a four wheeler:**
The probability \( P(\text{Four Wheeler}) \) is calculated using the formula:
\[ P(\text{Four Wheeler}) = \frac{\text{Number of Four Wheelers}}{\text{Total Number of Vehicles}} = \frac{126}{280} \]
Simplifying this fraction:
\[ P(\text{Four Wheeler}) = \frac{126 \div 14}{280 \div 14} = \frac{9}{20} \]

4. **Calculate the probability of selecting a two wheeler:**
The probability \( P(\text{Two Wheeler}) \) is calculated as:
\[ P(\text{Two Wheeler}) = \frac{\text{Number of Two Wheelers}}{\text{Total Number of Vehicles}} = \frac{91}{280} \]
Simplifying this fraction:
\[ P(\text{Two Wheeler}) = \frac{91 \div 7}{280 \div 7} = \frac{13}{40} \]

5. **Calculate the probability of selecting a three wheeler:**
The probability \( P(\text{Three Wheeler}) \) is calculated as:
\[ P(\text{Three Wheeler}) = \frac{\text{Number of Three Wheelers}}{\text{Total Number of Vehicles}} = \frac{63}{280} \]
Simplifying this fraction:
\[ P(\text{Three Wheeler}) = \frac{63 \div 7}{280 \div 7} = \frac{9}{40} \]

### Final Answers:
- (i) Probability of selecting a four wheeler: \( \frac{9}{20} \)
- (ii) Probability of selecting a two wheeler: \( \frac{13}{40} \)
- (iii) Probability of selecting a three wheeler: \( \frac{9}{40} \)