Consider 18- objects (distinct) then the probability that we can take odd number of objects in a draw is

Options

A. `1/2`
B. `1/4`
C. `1/8`
D. `1/16`

Explanation

To solve the problem of finding the probability of drawing an odd number of objects from a total of 18 distinct objects, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Total Objects**:
We have a total of 18 distinct objects.
\[ \text{Total objects} = 18 \]

2. **Determine Even and Odd Counts**:
We need to find how many ways we can draw an odd number of objects. The possible odd numbers of objects we can draw from 1 to 18 are:
- 1, 3, 5, 7, 9, 11, 13, 15, 17
This gives us a total of 9 odd numbers.

Similarly, the even numbers of objects we can draw are:
- 2, 4, 6, 8, 10, 12, 14, 16, 18
This also gives us a total of 9 even numbers.

3. **Establish Probability Relationship**:
Since the number of ways to draw an odd number of objects is equal to the number of ways to draw an even number of objects, we can denote:
\[ P(\text{odd}) = P(\text{even}) \]

4. **Use Total Probability**:
The total probability of drawing either an odd or an even number of objects must equal 1:
\[ P(\text{odd}) + P(\text{even}) = 1 \]

5. **Substitute the Equal Probabilities**:
Since \( P(\text{odd}) = P(\text{even}) \), we can substitute:
\[ P(\text{odd}) + P(\text{odd}) = 1 \]
This simplifies to:
\[ 2P(\text{odd}) = 1 \]

6. **Solve for Probability of Odd Draws**:
Dividing both sides by 2 gives us:
\[ P(\text{odd}) = \frac{1}{2} \]

### Final Answer:
The probability that we can take an odd number of objects in a draw is:
\[ \boxed{\frac{1}{2}} \]