I asked a Large Language Model the following question

Suppose that n >= 1 individuals attend a social gathering. An experiment is conducted where each individual is given a single ticket with a unique number printed on it. Once all n individuals have been given a ticket, the tickets are placed in a bag. Each individual randomly selects a ticket from the bag, with each ticket equally likely to be selected. Determine, with clear reasoning, the probability that at least one individual selects their own ticket.

It came back with the following answer, can you see what is wrong?

In this scenario, there are n individuals attending a social gathering, each given a unique ticket with a unique number. The tickets are placed in a bag and each individual randomly selects one ticket from the bag. The goal is to find the probability that at least one individual selects their own ticket.

The probability of any individual not selecting their own ticket is (n-1)/n. This is because there are n tickets in the bag and n-1 of them are not the individual's own ticket.

Therefore, the probability of an individual not selecting their own ticket is (n-1)/n.

The probability of all n individuals not selecting their own ticket is ((n-1)/n)^n. This is because the probability of an event happening multiple times is the product of the individual probabilities.

However, we want to find the probability of at least one individual selecting their own ticket, which is the complement of the probability of no one selecting their own ticket. Therefore, we can find the probability of at least one individual selecting their own ticket as 1 - ((n-1)/n)^n

As you can see, as n increases, the probability of at least one individual selecting their own ticket approaches 1, this is because as the number of people increases, the chances of having at least one person selecting his/her own ticket increases.

The error is the assumption that two individuals can select the same ticket which the wording of the question ensures is impossible.