Love statistics and want to learn about it more?
This blog will define statistics for you and offer an explanation to one of its most interesting and vital topic which is probability.
The reason for choosing probability in this blog is that most scholars are confused by it and has been observed as an area where most pupils make silly mistake frequently.
The nature and types of probability are one of the primary reason for confusion among disciples. Hence, this blog will explain these in detail along with certain other facts.
So, without any further delay in this matter, let’s start with statistics first and then move onto the rest of the matter.
What is statistics?
If you are interested in pursuing statistics then being clear about what it is and its concepts are crucial for scoring well in assignments and exams.
It refers to a mathematics branch that deals with collection of data along with its presentation after organizing, analyzing and interpreting it.
Now if census data is not available then statisticians develop particular experimental designs or survey samples that aid in retrieving whatever information is necessary.
Two primary statistical methods include inferential and descriptive statistics.
Inferential statistics involves drawing conclusions from collected data which are random variation’s subject while descriptive deals with summarizing data from any sample that uses indexes like standard or mean deviation.
Descriptive statistics frequently is concerned with two distribution property sets which maybe be population data or sample collected.
Central tendency searched for characterizing typical or central value’s distribution which dispersion will characterize extent of distribution depart members from each other and it’s center.
Now coming to mathematical statistics inferences, this is made under probability theory’s framework that deals random phenomena’s analysis.
This is just what statistics is all about. Without understanding this, it would be harder for you to create assignments on different topics of probability and more.
Let’s check probability now along with its types!
It refers to measuring an event that will take place. It quantifies a number which is between zero and one.
Here, zero might indicate impossibility of an event occurring and one indicating an event’s certainty.
The higher an event’s probability appears after calculation; it is more likely that an event will take place.
For instance, if you toss a coin, then there can be an outcome that it faces heads or tails as both events are equally probable.
As no other outcome is possible other than these two, you can write that each outcome has a chance of 50%.
Such concepts are given mathematical axiomatic formalization in theory of probability that is widely used in areas such as statistics, finance, mathematics, science, gambling, machine learning/A.I., game theory, computer science and many more.
Probability is also used for describing complex systems’ regularities and underlying mechanics.
Hence, probability has a huge application in everyday tasks. Now without getting more into that detail, you will now come across different types of probability that you should know about when opting for Statistics program.
Types of probability
- Classical probability
When learning about probability, one should always start with the classic concept of it.
This standard probability type can be easily demonstrated by considering what will happen when you will perform a coin toss or roll a dice pair.
Think about this, when a referee does a coin toss before a football match begins; it offers just two options tails or heads as these two are only outcome that can take place.
Odds of the coin landing on a particular side can be easily calculated if you determine every possible result which in this is two.
After this, you need to record what happens when each time when you toss that coin. You can do this for let’s say fifty times and then check what the result is.
From this, you can easily determine what the specific outcome of classical probability is.
In classical or standard probability, you declare that each experiment that involves statistics, there will be elements or aspects which will have exact chance of occurring.
If you try to roll dice then the outcome will be one of the six possibilities as a dice has six sides/numbers.
It is similar to the coin toss as no matter how many times you toss a coin in air, it will have either of two outcomes heads or tails.
To be perfectly clear, probability is same or equal to favorable outcomes’ number divided by possible results’ number.
- Experimental probability
Two things determine experimental probability; first, you will have to consider trials’ total number and second, outcomes’ total number which you have to take under your consideration.
Let’s demonstrate this with an example!
If you try rolling a quarter let’s say one hundred times and 40 times it falls on tails. Then you know that theoretical probability of it will be 0.4 or 40/100.
This probability then describes that a specific outcome occurring a number of times is divided by total trails’ number which was performed.
Next up is conditional probability!
- Conditional probability
It refers to probably a group of occurrence or events which are dependent on each other. It examines factors like past performances that normally would influence performance in future too so that a specific performance’s probability can be determined.
To put in simple words, conditional probability takes note of the entire picture and considers what are the outcomes in past events for determining the probability of future result.
This type measures occurrence of a particular scenario’s likelihood where another event has taken place by assumption, assertion, or evidence.
Let’s make it clear for you with the help of an example.
For instance, on a normal day likelihood of you having a sore throat can be of 5%.
However, if you know or assume the fact that if you suffer from the flu then you know already that conditional probability of you suffering from sore throat becomes a more likely situation.
So, you can describe this as likely of XYZ happening under a circumstance known as ABC, or P(XYZ/ABC), where P will stand for probability.
Also, XYZ and ABC are two different events. So, in above example, if you suffering from flu then having a chance of sore throat will increase to 75%.
- Markov Chain probability
This is similar to above explained conditional probability where it looks at events’ sequence and facts that every probability of these depends on things happened at events before or even an events’ set.
For example, let’s assume now is falling outside. You might wonder whether it will be still snowing in an hour. Depending on how much it snowed in the first hour, you can guess your answer.
This probability type utilizes matrixes for gaining extreme efficiency in probability. Also, you can use it to determine numerous things from certain weather conditions/patterns to the performance of your stock in stock market.
Whatever you start to discuss from football score to letters or numbers, always there will be a finite state’s number involved in it. Moreover, it is determined always by two aspects; first, current state and second, total time that has passed by.
This probability always contains a group of transitions. Such transitions are found by a probability distribution which satisfies stochastic procedure’s property which is called memoryless or Markov property.
- Standard probability
This always includes a comparison of how many different possible outcomes there might be along with how many times a singular outcome can occur within total number.
With this type of probability, you will need to look at particular events where first event will not affect outcome of second or third event.
- Subjective (Personal) probability
This is considered by many to be least reliable probability type as this happens to be based on a person’s reasoning and judgment.
With personal or subjective probability, the conclusion is based on a result that a person might expect to take place.
In this type, no interpretations or formal calculations are used. However, it centers around an individual’s knowledge and feeling on a particular subject.
For example, if you are watching a football or basketball match with friends, you might come up with a conclusion that team X will win.
This assumption by you might be made from the fact that you want team Y to win. However, it also may be the case that your conclusion is based on their current form or ranking.
Anyhow, this type of probability includes a person’s personal opinion as well as basic facts for forming a statement which makes an individual think that a specific team will win a match.
- Theoretical probability
This is considered to be one of easiest ways for determining a probability for something taking place. It is simply based on ABC’s possible chances of happening.
For instance, if you determine to figure out theoretical probability of whether a coin will be landing on tails or heads when tossed, then, first of all, you require knowing only two possibilities are possible.
So, when tossing a coin in air, two possibilities will occur tails or heads. Hence, theoretical probability of a coin you toss will land on head is one of two which you can demonstrate as 1:2.
You have to consider number of options which is two in this situation and basing theoretical probability on it.
Now if the coin had three sides, then head was just one possibility out of three or simply denoted as 1:3.
Now there is another way you can look at it!
Another way of this probability is saying that possibility of something taking place is equal. For example, a dice has six sides which offer six different numbers.
However, when you roll it, you can always come to the conclusion that all six sides have equal appearing chance.
- Relative frequency interpretation
In this probability, you need to start conducting a few particular experiments numerous times. After which you can base relative frequency on observation itself or actual measurement.
For instance, if you roll any dice let’s say 50 times and the number 5 comes up 20 times then relative frequency of number five will be 20/50
Now, moving on to the last type of probability which you will find in this blog is unconditional probability. Have a look!
- Unconditional probability
This probability type refers to a single independent chance which is one result will occur from total number of outcome samples which are possible.
If you are willing to find a situation’s unconditional probability then adding sum of outcomes of a particular scenario, then you should divide it but total possible outcomes.
If you look at a particular group of dogs and select one at random, that means that each dog who is in that group has same odds of getting picked by you.
Now if you decide to select a specific species of dog with certain qualities like color, size, etc. then odds will be little different naturally.
These are the different types of probability you will come across when studying statistics. Hence, understanding each of them is quite essential.
You like every other scholar might have assignment issues in probability because of the types and how each determines a specific result.
Hence, it is ideal for you to understand these in detail and get correct results for your assignment. Your professor can select a topic on any one of these probability types; hence, knowing about them all is necessary.
Since you went through this blog, you are aware of all the types available and things you should know about. This gives you a head start and if you are willing to learn more about in detail then opting for detailed research is ideal.
Evelyn W. Minnick is a renowned blogger and teacher who solves various issues of students and offers helpful advice that clears complex topics. She has completed her MBA from UCLA Anderson School of Management and has over 6 years of experience in teaching. This is why she is quite popular among scholars who need assistance with subjects like statistics.