There are 35 student in class IX A, 34 in IX -B &33 in IX C. If even roll numbers are allowerd project on chapter 2, Polymomials & odd roll number are allotted for chapter -1 , Number system . What is the probability that the student chosen
(i) Prepares project on chapter 1
(ii) Prepare project on chapter 2

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the total number of students.
We have students from three classes:
- Class IX A: 35 students
- Class IX B: 34 students
- Class IX C: 33 students

**Total number of students = 35 + 34 + 33 = 102 students.**

### Step 2: Determine the number of students with odd and even roll numbers in each class.

**Class IX A:**
- Total students = 35 (odd)
- Odd roll numbers = 18 (1, 3, 5, ..., 35)
- Even roll numbers = 17 (2, 4, 6, ..., 34)

**Class IX B:**
- Total students = 34 (even)
- Odd roll numbers = 17 (1, 3, 5, ..., 33)
- Even roll numbers = 17 (2, 4, 6, ..., 34)

**Class IX C:**
- Total students = 33 (odd)
- Odd roll numbers = 17 (1, 3, 5, ..., 33)
- Even roll numbers = 16 (2, 4, 6, ..., 32)

### Step 3: Calculate the total number of students with odd and even roll numbers.
- Total odd roll numbers = 18 (from IX A) + 17 (from IX B) + 17 (from IX C) = 52 students.
- Total even roll numbers = 17 (from IX A) + 17 (from IX B) + 16 (from IX C) = 50 students.

### Step 4: Calculate the probabilities.
(i) **Probability that a student prepares a project on Chapter 1 (odd roll numbers):**
- Probability = (Number of students with odd roll numbers) / (Total number of students)
- Probability = 52 / 102
- Simplifying: 52 / 102 = 26 / 51

(ii) **Probability that a student prepares a project on Chapter 2 (even roll numbers):**
- Probability = (Number of students with even roll numbers) / (Total number of students)
- Probability = 50 / 102
- Simplifying: 50 / 102 = 25 / 51

### Final Answers:
(i) The probability that a student prepares a project on Chapter 1 is **26/51**.
(ii) The probability that a student prepares a project on Chapter 2 is **25/51**.

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