I am a vicous man-killer when i am angry but I am gentle and calm when I am happy. I can be a home pet but my fangs dont suit the job. I have a legend about me but I know it might not be true.

I may look scary but I am not really that scary. I may walk into your garden but then I would tell a lie.

What am I ?

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?

At a particular ice cream van two types of ice creams are being sold. The small one costs 1 dollar, the big one 2 dollars. Marsha puts an amount of 2 dollars one the counter and gets without asking the big ice cream. Martha also would like to have an ice cream. She also puts an amount of 2 dollars on the counter. Then the ice cream seller asks her which ice cream she would like to have. Assuming that the persons do not know each other, how can you explain their behavior.