# Probability Theory

Simply speaking, probability relates to ascertaining what the chances are (in other words, what the odds are) of some event happening, such as winning a jackpot or drawing a certain card or hand. It is the figure obtained when you divide the number of ways an event can occur by the total possible number of outcomes in a given scenario. For example, if we wanted to establish the probability of drawing a red card from a deck of cards, we would divide 26 (total number of ways to draw a red card, since there are 26 red cards in a deck) by 52 (total number of cards in the deck, disregarding jokers), giving us ½ i.e. a probability of 0.5.

The logic behind probability theory has of course been around forever, though the actual mathematical study of it is a relatively new development. The extensive inherent probability scenarios that exist in the ancient pastime of gambling in particular were a major factor in prompting the study of probability in mathematical terms – people wanted to know in more precise detail what their chances of winning were!

## The mathematics of probability

The mathematics that describe the laws of probability involve events – represented by algebraic variables, usually “A” – and decimal numbers between 0 and 1. So, the probability (P) of event A (say, drawing a King from a deck of cards) happening is represented as “P(A) or p(A) or Pr(A). An event that has no chance of occurring (drawing five aces from a deck of cards) has a probability of zero, while an event that is certain to occur (drawing a card that is either red or black from a deck of cards without jokers) has a probability of 1.

To calculate the probability of two events occurring at the same time is simply a matter of multiplying together the probability of each of these events. For example, if we spun two dice at the same time, the probability of rolling a 4 on the one dice is one in six (P = 0.1667), while the probability of rolling a 2 on the other is also 0.1667, but the probability of rolling a 2 AND a 4 is 0.1667 x 0.1667 = 0.027. Various formulas for probability exist, and of particular importance in determining which formula to use is to ascertain whether events are independent or dependent.

Have a read through our other pages on the mathematics of gambling to learn about more applications of mathematics in gambling, or view our gambling mathematics glossary for a quick overview of the most important concepts in addition to probability theory.