here are 10 cards in a bag bearing numbers from 1 to 10. A card is drawn from the bag 60 times. Each time, the number obtained is noted and the card drawn is replaced. It was found that the card bearing number 7 was drawn 4 times. Now, if a card is drawn at random, find the probability of getting the card bearing number 7.

Answer

To find the probability of drawing a card bearing the number 7 from a bag of cards numbered 1 to 10, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the total number of draws:**
- A card is drawn from the bag 60 times. Each time a card is drawn, it is replaced back into the bag.
- Therefore, the total number of draws (or trials) is **60**.

2. **Identify the number of favorable outcomes:**
- It is given that the card bearing the number 7 was drawn **4 times** out of the 60 draws.
- Thus, the number of favorable outcomes (drawing a card with the number 7) is **4**.

3. **Calculate the total number of possible outcomes:**
- The total number of possible outcomes (the total number of draws) is **60**.

4. **Use the probability formula:**
- The probability of an event is calculated using the formula:
\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]
- Here, we need to find the probability of drawing a card with the number 7:
\[ P(7) = \frac{4}{60} \]

5. **Simplify the fraction:**
- To simplify \(\frac{4}{60}\), we can divide both the numerator and the denominator by their greatest common divisor, which is 4:
\[ P(7) = \frac{4 \div 4}{60 \div 4} = \frac{1}{15} \]

6. **Final answer:**
- Therefore, the probability of drawing a card bearing the number 7 is \(\frac{1}{15}\).