Mathematics book of class IX contains 15 chapters . A maths teacher asked one of the students to write the name of each chapter on slips , One name on one slip . She mixed the slips thoroughly in a box.
She called a student to pick up one of the slips . What is the probability that the written on its is from
(i) Geometry
(ii) Algebra

Options

A. (i) `(7)/(5)` (ii) `(2)/(15)`
B. (i) `(7)/(5)` (ii) `(1)/(15)`
C. (i) `(4)/(5)` (ii) `(2)/(15)`
D. (i) `(3)/(5)` (ii) `(4)/(15)`

Answer

To solve the problem, we will calculate the probability of picking a slip from the box that corresponds to a chapter in Geometry and then for Algebra.

### Step-by-Step Solution:

1. **Identify the Total Number of Chapters**:
- The total number of chapters in the mathematics book is given as 15.

2. **Identify the Number of Favorable Outcomes for Geometry**:
- We need to find out how many chapters are related to Geometry. According to the information provided, there are 6 chapters in Geometry.

3. **Calculate the Probability for Geometry**:
- The formula for probability is:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes}} \]
- For Geometry:
\[ \text{Probability of Geometry} = \frac{6}{15} \]
- Simplifying this fraction:
\[ \frac{6}{15} = \frac{2}{5} \]

4. **Identify the Number of Favorable Outcomes for Algebra**:
- Next, we find out how many chapters are related to Algebra. According to the information provided, there are 3 chapters in Algebra.

5. **Calculate the Probability for Algebra**:
- Using the same probability formula:
\[ \text{Probability of Algebra} = \frac{3}{15} \]
- Simplifying this fraction:
\[ \frac{3}{15} = \frac{1}{5} \]

### Final Answers:
- The probability that the chapter picked is from Geometry is \(\frac{2}{5}\).
- The probability that the chapter picked is from Algebra is \(\frac{1}{5}\).