Probability is a way of predicting an event that might occur at some point in the future. It is used in mathematics to determine the likeihood of something happening or if something happening is possible. There are three types of probability problems that occur in mathematics.
Probability as Counting
The most basic type of probability problem consists of a simple formula: amount of successful outcomes (divided by) amount of total outcomes. All you need are two numbers to determine probability. For instance, if an experiment has 20 total possible outcomes and only 10 of them are successful, the probability of that problem is 50 percent. This is the type of probability problem that occurs most in mathematics and everyday situations.
Probability in Geometry
A less common, but still basic problem of probability is in using geometry. In this kind of probability, there are too many possible outcomes to be expressed in a simple equation. This includes evaluating the number of points on a line segment or in a space, and what the probability of that space’s future points were it larger, as well as the probability of things happening in time. In order to do this equation, you need the length of the known region and divide it by the length of the total segment. This will give you the probability. For instance, if Bob parked his car in a parking lot at a randomly chosen time that has to fall somewhere between 2:30 and 4:00, and exactly half an hour later he drove his car off the parking lot, what is the probability that he left the parking lot after 4:00? For this problem, we divide the hours into minutes so that we are left with smaller fractions. Because there are an infinite number of times that Bob could have driven off the lot, there is no way to count exactly when it happened. We can calculate the probability that Bob drove away after 4:00 by comparing the line segments of successful outcome times to that of total outcome times. The length of possible segment times is 30 minutes because that is the time of successful outcomes. Then, divide that by the total amount of time between 2:30 and 4:00, which is 90 minutes. Take 30/90 to get a probability of 1/3, or 33 percent chance that Bob drove off after 4:00.
Probability in Algebra
The least common form of probability is the problems found in algebraic equations. This type of probability is solved by determining past events and how they affect potential future events. For instance, if the probability that it will rain in Seattle next Tuesday is twice the probability that it will not rain, the probability for rain next Tuesday in Seattle would be calculated by using an algebraic equation: Let x represent the probability that it will rain. This makes the equation [x=2(1-X)] since it either will or will not rain in Seattle. This makes the probability that it won’t [1-x]. This gives us the answer of 2/3 or 67 percent chance of rain.
Summary of Probability Problems
These problems and theories are based on the most essential aspects of probability. Because so many different circumstances prompt so many different possible outcomes, probability can become infinitely more difficult. However, these simple equations and explanations can be applied to any probability problem in some way to make them work.