Solution to: Two Trains
Obviously, the train drives as often to Nijmegen as to Venlo. However, that is not what Annette counts. She walks to the railroad track and waits until she sees the train. Apparently the chance that she sees the train to Nijmegen is five times as large as seeing the train to Venlo. The solution is in the time it takes until she sees a train. Suppose the train to Nijmegen always passes on the hour and on the half hour, and the train to Venlo passes at 5 and 35 minutes past the hour. Annette arrives at the railroad at a random moment within the half hour. Within that half hour there are 5 minutes in which she will see the train to Venlo first (1/6 chance) and 25 minutes in which she will see the train to Nijmegen first (5/6 chance). That is why Annette will see the train to Nijmegen five times as often as the train to Venlo.