Probability Theory

Probability theory

Probability theory is the statistical study of an uncertain or random event to determine its likelihood to happen. The chance of an event to occur is stated as a number between zero and one, whereby one indicates  high possibility(certain to happen) and zero indicated impossibility. The higher the probability number in an event, the higher the likelihood that the event will happen.

A good example of explaining probability is tossing a fair coin. Since the coin is unbiased, there is an equal possibility of the coin landing on heads or tails. In other words, there is a 50% chance of heads and 50% chance of tails. And since there is no other outcome that is expected from this experiment, the probability of the coin landing on either heads or tails is 50 %, which can be denoted as 0.5 or ½.

Understanding probability theory and its terminology

To understand probability, let’s consider an experiment that can be repeated and that can give us different results on different attempts but on similar conditions. All the possible outcomes in an experiment is statistically referred to as a sample space. In an experiment of tossing a coin, for instance, the sample space will have two possible outcomes; the heads and the tails. If we consider an experiment of tossing two dice, on the other hand, our sample space will have 36 possible outcomes.

In the aforementioned experiments, the outcomes can have either a discrete or continuous random variable. And what is a random variable, you may ask? A random variable is observed when the outcome has numerical values. They are of two types:

  • Discrete random variable: A discrete random variable is a variable that takes on a small number of distinct values like 0, 1, 2, 3, 4, 5…
  • Continuous random variable: This one takes a limitless number of distinct values. Measurements such as length often fall under continuous random variables.

Also, a probability test can be either independent or dependent. An event is considered dependent if its likelihood to occur rely on the likelihood of another event occurring. If an event does not rely on the probability of another event occurring, then it is said to be independent. Let’s consider our two experiment of tossing a coin and tossing two dices for instance. The probability of the coin landing on heads or tails is no way affected by the probability of the numbers displayed by the faces of the two dices. Hence these two events can be said to be independent of each other.

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Real life applications of probability theory

We use probability in our daily lives to determine what the likelihood of an event to occur will be especially for those events that we are not sure about the results. Sure, most of the time, we will not apply complex mathematical formulas or solve actual probability problems but we will use subjective probability to judge the situation and decide the best course of action. Below are some of the events in which probability theory is applied in real life.

  • Weather forecasting: The meteorology department can’t forecast exactly what the atmospheric conditions will be without probability. They have to use instruments and tools to determine the chances that there will be sunshine, rain, or snow. If 40 out of 100 days experience rain, for instance, then there is a 40% likelihood of rain. Meteorologists also use past data to estimate how high or low the temperatures will be in the future and other probable weather patterns.
  • Insurance options:Probability theory plays asignificant role in determining the best insurance policies for you and your family. For example, when selecting a motor insurance policy, you can use probability to analyze the likelihood that you will require to file a claim. For instance, if 20 out of 100 drivers (20% of drivers) in your area have hit a person over the past few months, you will likely consider a comprehensive cover for your car, not just liability.
  • Gaming: If you are playing a game that involves luck or chance, you will use probability to decide the most appropriate move. For instance, if you are placing a bet on football team, you may want to consider how many times the team you want to bet on has won the match over the past year.

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