Cards marked with numbers 3, 4, 5, .........,50 are placed in a box and mixed thoroughly. One card is drawn at random from the box, find the probability that the number on the drawn card is
a two digit number.

Answer

To solve the problem of finding the probability that the number on a randomly drawn card is a two-digit number, we can follow these steps:

### Step 1: Determine the total number of cards
The cards are marked with numbers from 3 to 50. To find the total number of cards, we can calculate the range of numbers:

- The smallest number is 3.
- The largest number is 50.

The total number of cards can be calculated as:
\[ \text{Total Cards} = 50 - 3 + 1 = 48 \]

### Step 2: Identify the two-digit numbers
Next, we need to find the two-digit numbers within the range of 3 to 50. The two-digit numbers start from 10 and go up to 50. The two-digit numbers are:
10, 11, 12, ..., 50.

To find the count of these two-digit numbers, we can calculate:
\[ \text{Two-digit Numbers} = 50 - 10 + 1 = 41 \]

### Step 3: Calculate the probability
The probability of drawing a two-digit number is given by the formula:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
In this case, the number of favorable outcomes (two-digit numbers) is 41, and the total number of outcomes (total cards) is 48. Therefore, the probability is:
\[ \text{Probability} = \frac{41}{48} \]

### Final Answer
Thus, the probability that the number on the drawn card is a two-digit number is:
\[ \frac{41}{48} \]

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