You have just moved to the Friedrich-Schiller-Studentenheim in Graz. You were told that there are two tram lines nearby: Line 7 runs on average every 5 minutes and line 1 runs on average every 10 minutes. Waiting for the tram for the first time at your closest tram station, you don't know which line it serves. You've been waiting for 7.5 minutes, and the tram hasn't arrived yet. Assume that the probability density function for the time interval between trams (at a station) is given by an exponential function (that is often used to model the time interval between independent events that happen at a constant average rate)

(1) |

where is the mean interval length, and .

- Use Bayes rule to derive the probability that you are waiting for a tram of line 7?
- After how many minutes of waiting would you believe that the tram you're waiting for is more probable of line 1?