Rat race

On the yearly fair you can play as often as you like the game "rat race". In this game a rat is freed at the beginning of a circuit. The rat will then run to hole A, B or C, every hole with equal chance. Before the rat is freed, you can bet any amount you like on the hole the rat will run into. If you choose the right hole, you'll get back twice the amount you've put a stake. If you're wrong you loose your money. Suppose you carry an infinite amount of money. Will you in that case always loose money playing this game, or does there exist a strategy to win money. Does this strategy also work in the more realistic situation when you carry a limited amount of money or if there is a maximum limit on the bet?

Air trip

At the same time two planes depart from JFK international airport. One plane flies exactly in northern direction, while the other one flies exactly to the east. Both planes fly at the same speed and at the same height. Which plane is after one hour the most far away from JFK?

Predicting share prices

What will be the probability that the price of a randomly choosen share that can be bought on the euronext stock exchange in Amsterdam, starts with the digit 1?