To find the probability that the next person who visits the website will purchase exactly one costume, we first need to determine the total number of visitors and the number of visitors who purchased exactly one costume.
From the information provided:
- Total number of visitors who purchased no costume: 314
- Total number of visitors who purchased exactly one costume: 68
- Total number of visitors who purchased more than one costume: 17
First, we calculate the total number of visitors:
\[ \text{Total Visitors} = \text{Visitors who purchased no costume} + \text{Visitors who purchased exactly one costume} + \text{Visitors who purchased more than one costume} \]
Substituting in the values we have:
\[ \text{Total Visitors} = 314 + 68 + 17 = 399 \]
Next, we can find the probability that the next visitor will purchase exactly one costume. The probability \( P \) is given by the ratio of the number of visitors who purchased exactly one costume to the total number of visitors:
\[ P(\text{exactly one costume}) = \frac{\text{Number of visitors who purchased exactly one costume}}{\text{Total number of visitors}} = \frac{68}{399} \]
Now, we should check if this fraction \(\frac{68}{399}\) can be simplified. To do this, we can check for the greatest common divisor (GCD) of 68 and 399.
The prime factorization of 68 is: \[ 68 = 2^2 \times 17 \]
The prime factorization of 399 is: \[ 399 = 3 \times 133 = 3 \times 7 \times 19 \]
Since 68 and 399 do not have any common factors, the GCD is 1. Therefore, \(\frac{68}{399}\) is already in its simplest form.
Thus, the probability that the next person will purchase exactly one costume expressed as a fraction in simplest form is:
\[ \boxed{\frac{68}{399}} \]