Cards marked with numbers `3,4,5……50` are placed in a box and mixed throughly. A card is drawn at random from the box, find the probability that the selected card bears a perfect square number.

Answer

To solve the problem of finding the probability that a randomly drawn card from a box marked with numbers 3 to 50 bears a perfect square number, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Range of Numbers**:
The cards are marked with numbers from 3 to 50.

2. **Count the Total Numbers**:
The total numbers from 3 to 50 can be calculated as follows:
\[ \text{Total Numbers} = 50 - 3 + 1 = 48 \]
So, there are 48 cards in total.

3. **Identify Perfect Square Numbers**:
We need to find the perfect squares between 3 and 50. The perfect squares are:
- \(2^2 = 4\)
- \(3^2 = 9\)
- \(4^2 = 16\)
- \(5^2 = 25\)
- \(6^2 = 36\)
- \(7^2 = 49\)

Thus, the perfect squares in this range are: 4, 9, 16, 25, 36, and 49.

4. **Count the Perfect Square Numbers**:
The perfect squares identified are: 4, 9, 16, 25, 36, and 49.
Therefore, the total number of perfect square cards is 6.

5. **Calculate the Probability**:
The probability \(P\) of drawing a card with a perfect square number is given by the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{48} \]

6. **Simplify the Probability**:
Simplifying \(\frac{6}{48}\):
\[ P = \frac{1}{8} \]

### Final Answer:
The probability that the selected card bears a perfect square number is \(\frac{1}{8}\).