Seven accidents occur in a week then what is the probability that they hapeen on the same day.

Answer

To find the probability that all 7 accidents occur on the same day of the week, we can follow these steps:

### Step 1: Understand the total number of days
A week consists of 7 days. Therefore, we have 7 possible days for the accidents to occur.

### Step 2: Determine the total outcomes
Each of the 7 accidents can occur on any of the 7 days. Hence, the total number of ways the 7 accidents can occur is given by:
\[ 7^7 \]
This is because for each accident, there are 7 choices (one for each day).

### Step 3: Determine the favorable outcomes
For all 7 accidents to happen on the same day, they can occur on any one of the 7 days. Thus, there are 7 favorable outcomes (one for each day).

### Step 4: Calculate the probability
The probability \( P \) that all 7 accidents occur on the same day is given by the ratio of the number of favorable outcomes to the total outcomes:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{7}{7^7} \]
This simplifies to:
\[ P = \frac{1}{7^6} \]

### Final Answer
Thus, the probability that all 7 accidents happen on the same day is:
\[ P = \frac{1}{7^6} \]