 # What is Probability In Math

Probability in simple words means possibility. The mathematical definition is that Probability is a measure of the likelihood of an event to occur. It can be expressed with a value from zero to one where zero indicates an impossibility to occur and one means the event has a very high chance of occurring. This is useful in probability distribution, where you will also need to know the total number of possible outcomes. Probability is not to be confused with the actual occurrence of the event. You can only predict the chances of the occurrence. It is a topic that is widely covered in the tenth grade in all schools in the UAE.

## Probability Formula:

The possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Also written as

Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes

### What are Equally Likely Events?

Equally likely events are those that have the same theoretical chances of happening within a sample space. For example, if you throw a die, then the probability of any of the numbers falling is 1/6 as all numbers have an equal chance. Complementary Events are those that have only two possible outcomes of either occurring or not. For example, it would either rain or not rain today. There can be no other possibility for this.

### Types of Probability

Let us briefly discuss the 4 types of Probability commonly taught in the schools of Dubai.

• Theoretical Probability is largely based on the logical sequence of events. It is founded on the possible chances of something happening. For example, if you toss a coin into the air, given that the coin has only 2 sides, the probability of either face will be 50:50.
• Experimental Probability is solely based on the observations of the experiment that is being conducted. It can depend upon the possible outcomes of the total number of trials conducted. For example, if a coin is tossed into the air 10 times, then all 10 results will be taken into consideration before determining the probability.
• Axiomatic Probability is derived from a set of rules called Kolmogorov’s three axioms. With this approach, the probability of the events can be quantified. Conditional Probability is the possibility of an event occurring based on an earlier event or conclusion.

### Probability Theory

J. Cardan, an Italian mathematician and physician first introduced the concept of probability through The Book on Games of Chance in the 16th century. The Probability Theory deals with the likelihood of the occurrence of certain events.

Although probability can be interpreted in many ways, it is best represented through a set of axioms or hypotheses that allow us to measure it between the values of zero and one. These are probability measures that help you to understand the possible results of the sample.

### Probability Density Function

The Probability Density Function (PDF) is a probability function that represents the density of a continuous random variable within a specific range of values. It helps to explain the normal distribution and the existence of mean and deviation. The standard normal distribution is commonly used in science to create a database or statistics for real-valued variables whose distribution is not known.

### Applications of Probability

Probability is something we intentionally or even unintentionally use in everyday life. From playing the lottery to a game of cards, throwing the dice, or selecting fruit from the bazaar, it is all linked to probability or even what we generally refer to as chance or luck. But it is actually a very simple mathematical event. Probability also has a wide variety of applications in other spheres of life such as predicting the weather, commercial and industrial risk assessment, and within the share market to predict rising or falling stock. It even extends to the sports sector where the probability of a team winning or losing is determined by its players and their strengths and weaknesses.

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