A range of natural phenomena such as the movement of molecules in liquids and gases, the fluctuation of stock prices and interest rates in financial markets, games of chance in a casino are modelled by repeated coin flippings aka the simple random walk - a sequence of random variables {S0, S1, . . . , Sn}. Upon investigation, we reach conclusions that play havoc with intuition. In a prolonged series of coin tossings, it is expected we stay positive about half the time, and in red the other half. This is entirely wrong, however. Several conclusions are drawn from the arc sine law.
References: [1] An introduction to probability theory and its applications, Volume I - William Feller