Previous Math Race

Exercise 4, 2015-2016 first edition

Exercise 4, 2015-2016 first edition

Christian and Anna are two secondary school students. Because they have not yet decided what to do after secondary school, they have decided to visit the open days at the University of Twente. After a day packed with information, they decide to walk back to their parking spot on campus. On the way back, they need to pass a small park with rectangular roads. That day they had been told that you can compute the number of ways in which you can walk through the park.

The park is shown schematically in the picture below. The blue spots are water, so you can’t go through those; only walking along their edges is possible. The brown line is a bridge over the water, which is passable.

Question A

If you assume that you can only travel horizontally to the right and vertically upwards over the edges, in how many ways is it possible to walk from point A to point B? Give an explanation please!

Question B

Suppose somebody is randomly choosing a route from A to B and each route is equally likely to be chosen. What are the odds that this person passes the bridge and travels the upper edge of lake L? Give an explanation please and round off to three decimal places.