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 two digit odd number ?

Options

A. 0.23
B. 0.45
C. 0.56
D. 0.34

Explanation

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

### Step 1: Identify the total number of cards
The total number of cards is equal to the total numbers from 1 to 100. Therefore, the total number of cards is:
\[ \text{Total cards} = 100 \]

### Step 2: Identify the two-digit odd numbers
Next, we need to find the two-digit odd numbers between 1 and 100. The two-digit numbers range from 10 to 99. The odd numbers in this range can be listed as follows:
- The first two-digit odd number is 11.
- The last two-digit odd number is 99.

The sequence of two-digit odd numbers is:
\[ 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99 \]

### Step 3: Count the two-digit odd numbers
To count the two-digit odd numbers, we can observe that they form an arithmetic sequence where:
- The first term \( a = 11 \)
- The common difference \( d = 2 \)
- The last term \( l = 99 \)

To find the number of terms \( n \) in this sequence, we can use the formula for the nth term of an arithmetic sequence:
\[ l = a + (n-1)d \]
Substituting the values:
\[ 99 = 11 + (n-1) \cdot 2 \]
\[ 99 - 11 = (n-1) \cdot 2 \]
\[ 88 = (n-1) \cdot 2 \]
\[ n-1 = 44 \]
\[ n = 45 \]

Thus, there are 45 two-digit odd numbers.

### Step 4: Calculate the probability
The probability \( P \) of drawing a two-digit odd number is given by the ratio of the number of favorable outcomes (two-digit odd numbers) to the total number of outcomes (total cards):
\[ P(\text{two-digit odd number}) = \frac{\text{Number of two-digit odd numbers}}{\text{Total number of cards}} = \frac{45}{100} \]
Simplifying this fraction:
\[ P(\text{two-digit odd number}) = 0.45 \]

### Final Answer
The probability that the card drawn has a two-digit odd number is:
\[ \boxed{0.45} \]