A, what is the probability that two people have stayed in three hotels and just two people have stayed in the same hotel?

The three hotels are: 1, No.2 and No.3.

A The probability of staying in any of the three hotels is 1/3.

Similarly, the probability of B staying in any of the three hotels is 1/3.

Then the probability of Party A and Party B staying at the hotel 1 is (1/3) * (1/3) =1/9.

Then the probability of Party A and Party B staying in Hotel II is (1/3) * (1/3) =1/9.

Then the probability of Party A and Party B staying in Hotel III is (1/3) * (1/3) =1/9.

Then the probability of two people staying in the same hotel is the sum of the three: 1/3.

Simply put, you can think like this:

The first, second and third hotels must have a hotel.

Then there is a 1/3 chance that A will live with A.