Applied Mathematics

Probability Theory

What are some examples in which probability is used?

There are thousands of examples in which probability is used, some are familiar, and some originate from the seamier side of life. For example, everyone has played at coin tossing at one time or another. Although there is no such thing as an idealized coin— a circular one of zero thickness—most coin tosses use the coins available, with either side face up (“heads” or “tails”; also phrased “heads up/down” or “tails up/down”). Thus, one can think of a coin as a two-sided die in lieu of the six-sided cubes we are all used to in a game of dice. If a coin is tossed with a good amount of spin, we can denote the two possible results as H for heads and T for tails. If we repeat the tosses N number of times, we obtain N(H) heads and N(T) tails. Thus, the fraction of N(H)/N and N(T)/N can be thought of as the chance (probability) to get a head or tail, respectively; P(H) and P(T) are the most common notations that represent the probability to get heads and tails, respectively. If we toss the coin many, many times, the result should be close to 0.5. Of course, this means that if we bet on the chances of heads and tails, we will not be much of a winner if we play too many games—and we will have to have really good luck to win if we play fewer games.


This is a web preview of the "The Handy Math Answer Book" app. Many features only work on your mobile device. If you like what you see, we hope you will consider buying. Get the App