5 Chapter 5 – What’s The Probability?
5.1 – Origins and Foundations
The probability of something occurring is the chance that it happens described by a number between 0 and 1 (including the possibility of 0 or 1). You’ve might have asked about the chances of something happening and received a response of 50%. This means that the chance that it happens is the same as the chance that it doesn’t happen. What would you think the chance of a light being on and off at the same time is? If you answered 0, you’re starting to understand what probability is. If the probability of something happening is 0, then it doesn’t happen. If the probability of something is 1, then it must happen.
Probability theory is the foundation of statistics. It’s a beautiful and deep subject in mathematics, but the basic ideas are not difficult to grasp. So, we will work on getting a firm grip on the fundamental concepts, and then we’ll use those concepts in a way which, hopefully, won’t overwhelm the reader with details.
Much of the early history of probability theory comes from games of chance. Games involving dice, cards, spinners, and other devices that create the element of chance and make the game exciting. People have bet money and possessions on these games since the games were first developed. The lure of winning a large sum of money or goods on the roll of two dice is hard to resist, and it’s easy to lose more money than one wins. So, people have studied the outcomes of repeatedly rolling the dice or drawing cards and come to the conclusion that certain dice rolls and certain card draws are more or less likely. These observations are the beginning of probability theory and statistics.
Some games are designed so that the best an individual can do when playing the game is to lose as little as possible. Each casino in Las Vegas NV makes about $21.5 million per day! How do they manage to make that much money from the people who patronize those casinos? They don’t charge an entrance fee, and they’re not making too much money on anything other than gambling. So, one might think that no one would go to a casino if they were going to lose a lot of money. Yet the patrons lose more money than they win. How does that happen?
There are two factors that make casinos the money machines that they are: 1) The chances that the casino (also called “the house”) wins is, overall, only slightly greater than 50% of the time, and 2) The number of people who go to the casino over a year’s time is very large. Since the chances of the casino winning is a bit more than 50% of the time, the chance of the patron winning is a bit less than 50% of the time. However, if many patrons are betting, then many will win. So, it’s virtually impossible for the patron to detect how often the casino wins compared to how often the patrons are winning, especially with the deleterious effects of alcoholic beverages.
From these games of chance, humans adapted and expanded the concepts of probability to business