In 1000 lottery tickets there are 5 prize winning tickets. Find the probability of winning a prize if a person buys one ticket.

Answer

To find the probability of winning a prize when a person buys one lottery ticket, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Number of Tickets**:
The total number of lottery tickets is given as 1000.

2. **Identify the Number of Winning Tickets**:
The number of prize-winning tickets is given as 5.

3. **Define the Probability Formula**:
The probability (P) of an event is calculated using the formula:
\[ P(\text{winning}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

4. **Substitute the Values into the Formula**:
Here, the number of favorable outcomes (winning tickets) is 5, and the total number of outcomes (total tickets) is 1000. So we substitute these values into the formula:
\[ P(\text{winning}) = \frac{5}{1000} \]

5. **Simplify the Fraction**:
To simplify \(\frac{5}{1000}\):
\[ P(\text{winning}) = \frac{5 \div 5}{1000 \div 5} = \frac{1}{200} \]

6. **Convert to Decimal Form**:
To express the probability in decimal form:
\[ P(\text{winning}) = 0.005 \]

### Final Answer:
The probability of winning a prize if a person buys one ticket is \( \frac{1}{200} \) or \( 0.005 \).

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