Suppose everyone behave at random, deciding with probability 0.1 to visit a hotel among 5 hotels on any given day.
The question is: The probability of the two people (A and B) visiting the same hotel on day 1 and day 2 under two conditions respectively as follows:
The hotels can be different on different days.
My answer is : $(0.1^2\times\frac{5}{5}\times\frac{1}{5})^2$
- $0.1^2$ means the chances of two people visiting a hotel on any given day
- $\frac{5}{5}\times\frac{1}{5}$ means the chances of choosing the same hotel. A has 5 hotel choices and B has 1 choice after A has chosen a hotel.The total number of hotels A and B can pick is $5\times5$.
- The out square is for 2 days since the event of two people visiting the same hotel on any given day is independent.
The hotels must be the same on different days.
My answer is : $(0.1^2\times\frac{5}{5}\times\frac{1}{5})\times(0.1^2\times\frac{1}{5}^2)$
- The $\frac{1}{5}^2$ means that they have only 1 choice on the second day since they have already chosen the hotel on the first day.
Am I right?