Search today’s topic is probability and probability is one of the most important topics of mathematics. It is present in the curriculum of lower as well as higher classes. Because it helps us in many ways, like from solving mathematics problems to a real-life situation. The probability is everywhere. That is why it is as one of the most important topics of mathematics let’s discuss what really probability is and what are their types of probability and how they can help us in solving mathematics problem as well as real-life problems
So you must have a little bit idea about probability really is but keeping that aside we should first discuss what it really is so basically probability means possibility yeah you can say that in the short term that possibility of getting something done or the possibility of solving some problem or the possibility of doing something can be solved out with the help of probability. And also there are many different types of probability which we will be discussing below.
As we have discussed above, it is one of the most important branches of mathematics and it deals with the occurrence of random events that means if some event is one occur or not or what is the percentage of occurrence of that particular event. Whether it may be in problems or it may be in real-life situations.
And the value of probability for occurring of a random event is always expressed between 0 and 1 so basically from all this above information we can say that the probability was introduced in mathematics for getting to know about the occurrence of some events or we can say that it helps us to predict how likely events are going to happen which basically means the occurrence of any random event overall it deals with random events’ occurrence.
More About Probability
There is a basic theory associated with branch Probability and that is that the meaning of probability is basically the chances of something which is likely to happen which is the same thing as above and that is the possibility of occurrence of an event. And all and all this is also the probability theory which is also used in the probability distribution.
In the theory of the probability distribution, you will learn that probability of sum outcome from any random experiment is based on the probability of any single element that is occurring from the number of Total possible events
You can also say that to find the probability of any given situation. We need to know about the total possible outcomes of that situation. Only then we can know about the probability of a single event that will be occurring from those situations
And one of the most important things in Probability is that the probability of all the events. That are happening in any situation sums up to 1.
This is one of the most important things to know or to remember whenever you are working on a probability problem or a real-life situation that involves probability to get it solved.
So you should always keep in mind that if the total sum of the situation is coming more than one then there is something wrong with the work you have done.
For example, whenever we are going to Toss a Coin there can be only two outcome either head or tails there is no chance that both of these outcomes are gonna come at one time show the only two possible outcomes are head and Tails
But when we toss 2 coins together in their there are three possibilities that can Aakar like both the coins can be heads or both the coins show tails or from both of those coins either one can be head and another can be tail so this is one of the important examples of the probability we can say that it is important in common example of probability this is how we know what can be the outcomes from any situation and this is how we will get to know about the probability of a single event from the series of events.
Formulae of the Probability
Now as we already discussed the probability Knights time to get to know about the formula of probability the basic and simplest formula a probability which is used everywhere
Show the formula of probability e is defined as the possibility of the element which is occurring is equal to the ratio of a number of favorable outcomes and the number of Total outcomes which means the probability of an event P(E) is equal to the number of favorable outcomes divided by the total number of the outcome of that situation.
P(E)= number of favorable outcomes / total number of outcome
Now as we have already discussed what probability is and good is the common and basic formula of the probability now it’s time to discuss about the types of probability yeah you read it right there is not colleges single type of probability there are three major types of abilities and those are
So there were the three major type of probability that we are going to discuss: –
Theoretical probability is based on the chances of something to happen we can also say that it is based on the possible chances of things to happen in a particular problem or a real-life situation with probability e is basically based on the basic reasoning open probability
It is conceptually one of the simplest situations but how this situation is a bit Limited because this situation does not have finitely many equally likely outcomes
For example let’s suppose we are tossing a coin and as we have discussed above that the single coin has only two outcomes either it shows heads or it shows tails. So the probability of getting head or a tail is equal and that is 0.5
So this was all about one of the most common or basic types of probability i.e, theoretical probability.
Now you already know about types of probability and that was theoretical probability now it’s time to discuss experiment probability The name suggests that is experimental it means it will consist of some experiments in this type of probability so basically we can say that the experimental probability is based on the basis of the observation that is coming from an experiment.
So in order to get an answer from such a type of probability there must be an experiment going on and from that we will account or observe the outcomes and then we will get to know about the probability of any event from that particular experiment.
The experimental probability can be counted as the number of the possible outcomes as always by the number of trials because we are doing an experiment and experiments are based on different trials so the experimental probability will be equal to two possible outcomes by the total number of trials.
For example, if we Toss a Coin 10 or 15 times then the 10 or 15 times are the trials and now how it will get done.
So let’s suppose we toss it 10 times and the head is recorded 7 times then the experimental probability of the head will be 7/10 and the experimental probability of tails will be 3/10.
By now you already know about theoretical and experimental probability
Now it’s time to discuss Axiomatic Probability.
So in axiomatic probability, there is a set of rules or we can call those set of rules as axioms which get applied to all the types reasons for a set of rules are known as
Kolmogorov’s three axioms. With the help of axiomatic probability, we can calculate the chances of occurrence and non-occurrence of any event.
And The axiomatic perspective says that probability is any function (we can call it P) from events to numbers satisfying the three conditions (axioms).
And those three conditions are:-
The three axioms of probability
- 0 ≤ P(E) ≤ 1 for every allowable event E. (In other words, 0 is the smallest allowable probability and 1 is the largest allowable probability).
- The certain event has probability 1. (The certain event is the event “some outcome occurs.” For example, in rolling a die, a certain event is “One of 1, 2, 3, 4, 5, 6 comes up.” In considering the stock market, a certain event is “The Dow Jones either goes up or goes down or stays the same.”)
- The probability of the union of mutually exclusive events is the sum of the probabilities of the individual events. (Two events are called mutually exclusive if they cannot both occur simultaneously. For example, the events “the die comes up 1” and “the die comes up 4” are mutually exclusive, assuming we are talking about the same toss of the same die. The union of events is the event that at least one of the events occurs. For example, if E is the event “a 1 comes up on the die” and F is the event “an even number comes up on the die,” then the union of E and F is the event “the number that comes up on the die is either 1 or even.”
So this was about the different types of probability and those were the Theoretical, Experimental, and axiomatic probability. Now you know about what probability is and what are the types of probability and there is a formula for finding the probability of an event and that is given below:-
Formulae for the probability of an event
You already know about what probability is and what are the types of probability now you should know about one of the most important formulae. Which is used many times in the branch of probability and regardless of the types of probability this formula is used everywhere.
P(E) = r/n
P(E’) = n-r/n = 1-r/n
So, P(E) + P(E’) = 1
This means that the total number or sum of probability can never be more than one.
As we have already discussed above
So, this was all about the probability and the different types of probability. We hope that by reading this blog you will get all the essential knowledge needed for working in a branch of probability or if you are a student then this blog must help you with providing the important knowledge about probability. So that you can get the most out whenever you study probability and the different types of probability. Get the best probability assignment help from our experts