When we talk about a probability, we talk about how something is likely to happen. The idea of probability is much to do about studying chances. It’s a part of mathematics that ascertains how one event might or might not happen.
Probability, however, is just a guide so studying it will not guarantee something happening. Tossing a coin and throwing dices are two of the most common examples.
Basic Types of Probability
Classical Probability
This is a very common type of probability and can be demonstrated most easily by considering what happens when you roll a pair of dice or toss a coin in the air. When a referee tosses a coin at the beginning of a football game, and it lands on the field, only two possibilities will occur, heads or tails.
The odds of it falling on a certain side can be calculated by determining all of the possible outcomes (in this case, only two), and then, by recording what actually happened each time you tossed that coin. In other words, you can toss the coin 10, 20, or 50 times, then write down what each outcome was, and you can determine what the classical probability of a certain outcome is.
In classical probability, you are declaring that in every experiment involving statistics, there are going to be elements that each have the same chance of happening. If you roll one die, which has six sides, the chances are equal that it will land on one of the six numbers, just like a coin toss is going to result in the same probability of ending up on either tails or heads every time. In other words, the probability is equal to the number of favorable outcomes divided by the number of possible outcomes.
Conditional Probability
This type of probably considers a group of events that are, in essence, dependent on one another. It looks at things such as past performance, which normally influences performances later on, so that the probability of that specific performance can be determined. In other words, it looks at the whole picture and takes into consideration what has happened in the past to determine what might happen in the future. Conditional probability measures the likelihood of a particular situation happening whereby another even has occurred, either by evidence, assumption, or assertion.
Let’s say that on any given day, the likelihood that an individual might have a sore throat is 5%. That is all well and good, but if you assume or know for a fact that that individual is suffering with the flu, you already know that the conditional probability of him or her also having a sore throat is much more likely. It can be described like this: the likely of ABC happening under the circumstances known as XYZ, or P(ABC/XYZ), where P stands for probability, and ABC and XYZ are the two events. In the above example, the chance that the individual with the flu is also suffering with a sore throat can go up to 75%.
Experimental Probability
The experimental probability of something happening is determined by two things. First, the total number of trials has to be considered. Second, the total number of outcomes is taken into consideration. If you roll a quarter 100 times and it lands on tails 40 of those times, your theoretical probability is going to be 40/100, or 0.4. This probability describes the number of times a certain outcome happened divided by the number of trials that were performed.
Markov Chain Probability
With similarities to conditional probability, a Markov chain probability looks at sequences of events and the fact that each of these probabilities depends on what happened in a prior event or even a set of events. If it is snowing outside, and you’re wondering if it is still going to be snowing an hour or three hours from now, you can base your guess on how much it is snowing in that first hour.
Markov chain probability uses matrixes to gain more efficiency in the probability, and it can be used in determining everything from specific weather patterns to how well your stocks will perform. Whatever you are discussing, be it football scores or certain numbers or letters, there is always a finite number of states involved, and it is always determined by (1) the current state (e.g., it is snowing outside), and (2) the amount of time that has elapsed (e.g., one hour).
Markov chain probabilities always consist of a set of transitions. These transitions are determined by a probability distribution that satisfies the Markov property, or the property of a stochastic process that is known as “memoryless.”
Personal (Subjective) Probability
This is perhaps the least reliable type of probability because it is based on someone’s personal judgment and reasoning. With subjective, or personal probability, the probability is based on an outcome that an individual expects to happen. No formal calculations or interpretations are used, but the probability essentially centers around one person’s feelings and knowledge on the subject.
For instance, if you’re watching a basketball or hockey game with some friends, you may declare at the beginning of the game that Team A will win. This assumption may be based on the fact that you want that particular team to win, but it can also be based on things such as their current rankings. In any case, subjective probability involves both basic facts and the person’s subjective opinions to form a statement that you think that certain team is going to win.
Relative Frequency Interpretation of Probability
In the relative frequency interpretation of probability, you start by conducting a certain experiment many different times, and then base the relative frequency on the actual measurements or on the observation itself. For example, if you roll a die 50 times and the number four comes up 15 times, the relative frequency of the number four is 15/50.
Standard Probability
Probability always involves comparing how many possible outcomes there are to how many times a certain outcome might occur within that total number. With standard probability, you have to look at specific events whereby the first event never affects the second or third event’s outcome.
Theoretical Probability
This is one of the easiest ways to determine the probability of something happening. It is based on the possible chances of XYZ happening. If you’re trying to figure out the theoretical probability that a coin is going to land on either heads or tails, you have to first know that only these two possibilities will occur.
In the tossing of a coin, there are only two possibilities, heads or tails, and, therefore, the theoretical probability that your coin toss will result in the coin landing on heads is one in two, which is also demonstrated as 1:2. You’re taking into consideration the number of options (in this case, two) and basing the theoretical possibility on that premise. If the coin had three sides and heads was one of the three possibilities, landing on heads would be a one-in-three possibility, or 1:3, in this instance.
Another way to look at theoretical probability is to say that the possibility of something happening is equal. A die has six sides, and when you roll one so you can view the result, you can say that all six sides have an equal chance of appearing.
Unconditional Probability
This type of probability refers to the single independent chance that a single outcome will result from a total sample of outcomes that are possible. If you want to find an event’s unconditional probability, you can add the sum of the outcomes of that particular event, then divide by the total number of outcomes possible. If you are viewing a group of people and select someone at random, this means each person in that group has the same odds of being chosen. If you decide to select a woman, or an individual within a certain age range, the odds are, quite naturally, a little different.
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