Cards on which numbers 1, 2, 3 .......... 100 are written (one number on one card and no number is repeated), put in a bag and are mixed thoroughly. A card is drawn at random from the bag. Find the probability that card taken out has
What is the probability that card taken out has a odd number ?

Options

A. 0.25
B. 0.49
C. `0.50`
D. 0.51

Explanation

To find the probability that a card drawn from a bag containing cards numbered from 1 to 100 has an odd number, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Cards:**
The total number of cards is 100, as they are numbered from 1 to 100.

2. **Determine the Total Number of Odd Numbers:**
The odd numbers between 1 and 100 are: 1, 3, 5, 7, ..., 99.
This forms an arithmetic sequence where:
- The first term (a) = 1
- The last term (l) = 99
- The common difference (d) = 2

To find the number of terms (n) in this sequence, we can use the formula for the nth term of an arithmetic sequence:
\[ l = a + (n - 1) \cdot d \]
Plugging in the values:
\[ 99 = 1 + (n - 1) \cdot 2 \]
\[ 99 - 1 = (n - 1) \cdot 2 \]
\[ 98 = (n - 1) \cdot 2 \]
\[ n - 1 = 49 \]
\[ n = 50 \]
Therefore, there are 50 odd numbers between 1 and 100.

3. **Calculate the Probability:**
The probability (P) of drawing an odd number can be calculated using the formula:
\[ P(\text{odd number}) = \frac{\text{Number of odd numbers}}{\text{Total number of cards}} \]
Substituting the values:
\[ P(\text{odd number}) = \frac{50}{100} \]
Simplifying this gives:
\[ P(\text{odd number}) = 0.5 \]

4. **Conclusion:**
The probability that the card drawn has an odd number is 0.5.

### Final Answer:
The probability that the card taken out has an odd number is **0.5**.

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