In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Tallulah sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.

Question

171 visitors purchased no costume.
148 visitors purchased exactly one costume.
34 visitors purchased more than one costume.

Based on these results, express the probability that the next person will purchase more than one costume as a fraction in simplest form.

Answer 1

To find the probability that the next person will purchase more than one costume, we first need to determine the total number of visitors who purchased costumes.

1. Total visitors:

   • Visitors who purchased no costume: 171
   • Visitors who purchased exactly one costume: 148
   • Visitors who purchased more than one costume: 34

   To find the total number of visitors, we sum these three groups:

   \[ \text{Total visitors} = 171 + 148 + 34 = 353 \]

2. Calculating the probability: We need to find the probability that the next visitor will purchase more than one costume. This can be found using the formula:

   \[ P(\text{more than one costume}) = \frac{\text{Number of visitors who purchased more than one costume}}{\text{Total number of visitors}} \]

   Substituting in the values:

   \[ P(\text{more than one costume}) = \frac{34}{353} \]

3. Simplifying the fraction: We need to check if the fraction \( \frac{34}{353} \) can be simplified. We look for the greatest common divisor (GCD) of 34 and 353:

   • The prime factorization of 34 is \( 2 \times 17 \).
   • The number 353 is a prime number and not divisible by either 2 or 17.

   Since 34 and 353 share no common factors (other than 1), the fraction \( \frac{34}{353} \) is already in its simplest form.

Thus, the probability that the next person will purchase more than one costume is:

\[ \boxed{\frac{34}{353}} \]