PPT Slide
Some problems to think about ….
4. The drunken sailor problems (***)
There is a drunk man coming out of a pub. He canot control his steps, and randomly (with 1/2 probability makes a step forward and backward, Let us assume that the length of his steps is fixed (1 m).
A. Determine the probability, that after N steps he is at a distance L from the starting point.
5. The problem 4.B in 2D and 3D (***)
Difficulty levels: (*) easy ; (**) medium ; (***) hard ; (!) don’t even try...
1. How to win a Mercedes (*)
There is a TV show in which a competitor can win a Mercedes with the help of a quizmaster (referee) if he/she is lucky. The rules are the following. (1) There are three doors, and the Mercedes is hidden behind of them. (2) The competitor can choose one door and point to it. (3) The quizmaster (who knows where the Mercedes is) will than will open one of the remaining doors, behind which there is no Mercedes. (4) The competitor than has the chance to choose again between the remaining two doors.
A. What is the best tactic that the competitor should follow. Should he/she remain with it’s first choice, or should he/she change to the door where the Mercedes can still be?
B. What are the probabilities of winning the Mercedes in both cases?
2. Getting a clemency (***)
In a jail there are three prisoner condemned to death (John, Peter and Paul). The news came that one of them will get a clemency, but the name is kept secret. The guard knows who will get a clemency. John understandably would like to find out who will get clemency, and asks the guard. Since the guard cannot furnish this information, he can only tell to John who is the one from the other two prisoner (Peter and Paul) who will not get the clemency. This is information in fact is totally useless to John, because he knew from the beginning that one of the other two will not get a clemency. BUT, anyhow, it seems that this useless information increased a lot the surviving chances of John. His original chances were 1/3, and now it seems his chances are 1/2. Is this right? What are the surviving chances of the other two after this seemingly useless information?
3. Physics student with two girlfriends (**)
John is a physics student with two girlfriends. The two girlfriend (Mary and Betty) are living at the two opposite end of a subway line. John loves both of them, and wants to visit them in an equal way. He don’t wants to bother himself with keeping a tight schedule, and decides to live the order of visit on chance. His plan is the following. He knows that the trains are living at the same time from the two endpoint in regular 5 minute intervals. He decide that each day he will go out to the subway station which is nearby his home in a random time between 5 and 6 pm. He will than take the first train that comes to the station. If this will take him to Mary he goes there, if it is taking him to Betty he goes there. So far so good, and he does this for a whole year. BUT after a year he observes that he visited Mary much-much more time than Betty. After two year this situation persists…and Betty leaves him…. What went wrong with his argument? How it could happen that Mary was visited much more often than Betty, since they both had the same chances ?