To know the opinion of 35 students about sixth subject as automobile engineering or financial management a survery was done . The data is recorded in the following table in favour of choosing automobile engineering .
No of students like 20
Dislike 15
Find the probability that a student will opt.
(i) automobile engineering
(ii) Financial management

Options

A. (i) `(4) /(7)` (ii) `(3)/(7)`
B. (i) `(4) /(7)` (ii) `(4)/(7)`
C. (i) `(3) /(7)` (ii) `(3)/(7)`
D. (i) `(3) /(7)` (ii) `(4)/(7)`

Answer

To solve the problem, we need to calculate the probability that a student will opt for either Automobile Engineering (AE) or Financial Management (FM) based on the survey results.

### Step-by-Step Solution:

1. **Identify the Total Number of Students:**
The total number of students surveyed is given as 35.

2. **Determine the Number of Students Who Prefer Each Subject:**
- Number of students who like Automobile Engineering (AE) = 20
- Number of students who dislike AE (which means they prefer Financial Management) = 15

3. **Calculate the Probability of Choosing Automobile Engineering (AE):**
The probability (P) of choosing AE is calculated using the formula:
\[ P(AE) = \frac{\text{Number of students who like AE}}{\text{Total number of students}} \]
Substituting the values:
\[ P(AE) = \frac{20}{35} \]
To simplify this fraction, we can divide both the numerator and the denominator by 5:
\[ P(AE) = \frac{20 \div 5}{35 \div 5} = \frac{4}{7} \]

4. **Calculate the Probability of Choosing Financial Management (FM):**
The probability (P) of choosing FM is calculated similarly:
\[ P(FM) = \frac{\text{Number of students who like FM}}{\text{Total number of students}} \]
Substituting the values:
\[ P(FM) = \frac{15}{35} \]
To simplify this fraction, we can divide both the numerator and the denominator by 5:
\[ P(FM) = \frac{15 \div 5}{35 \div 5} = \frac{3}{7} \]

### Final Answers:
- Probability of choosing Automobile Engineering (AE) = \(\frac{4}{7}\)
- Probability of choosing Financial Management (FM) = \(\frac{3}{7}\)