In a fair at a game stall, slips marked with numbers 3,3,5,7,7,7,9,9,9,11 are placed in a box. A person wins if the mean of numbers are written on the slip. What is the probabilty of his losing the game?

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Identify the numbers on the slips
The slips in the box are marked with the following numbers:
3, 3, 5, 7, 7, 7, 9, 9, 9, 11.

### Step 2: Calculate the mean of the numbers
To find the mean, we need to sum all the numbers and then divide by the total number of slips.

- **Sum of the numbers**:
\[ 3 + 3 + 5 + 7 + 7 + 7 + 9 + 9 + 9 + 11 = 70 \]

- **Total number of slips**:
There are 10 slips.

- **Mean**:
\[ \text{Mean} = \frac{\text{Sum of the numbers}}{\text{Total number of slips}} = \frac{70}{10} = 7 \]

### Step 3: Determine the winning condition
A person wins if they draw a slip with the mean value, which we calculated to be 7.

### Step 4: Identify the losing conditions
The person loses if they draw any slip that is not 7. The slips available are:
- 3 (2 times)
- 5 (1 time)
- 7 (3 times)
- 9 (3 times)
- 11 (1 time)

The losing slips are 3, 5, 9, and 11.

### Step 5: Count the losing outcomes
- The number of slips that are not 7:
- 3 appears 2 times
- 5 appears 1 time
- 9 appears 3 times
- 11 appears 1 time

Total losing slips:
\[ 2 + 1 + 3 + 1 = 7 \]

### Step 6: Calculate the probability of losing
The probability of losing is given by the ratio of the number of losing outcomes to the total number of outcomes.

- **Total outcomes**: 10 (total slips)
- **Losing outcomes**: 7

Thus, the probability of losing is:
\[ \text{Probability of losing} = \frac{\text{Number of losing outcomes}}{\text{Total outcomes}} = \frac{7}{10} \]

### Final Answer
The probability of the person losing the game is \(\frac{7}{10}\).

---