At any point, while studying maths you must have faced one problem or the other. Then you have gone to your teacher to solve your problem. It is difficult for you to reach out to your teacher can go with an online platform to study. There are many confusing topics of maths, probability is one of the most confusing topics ever. Probability is the possibility of occurrence of any random event. This topic is introduced in Maths to know how many times an event can happen and it’s value is between zero to one.
Meaning Of Probability:- Probability is the measure used to find the chances of occurrence of any event. There are many events whose prediction is not possible. The zero means that there is no possibility of any kind of occurrence in the event. The one says that there is a certainty for the event. It always lies between zero and one. Let’s understand probability more precisely with the help of an example.
If we toss a single coin then there can be only two possible outcomes I.e.. either heads or tales. You toss two coins simultaneously there the chances of possible outcome is three I.e.. two heads, two tales, one head, and one tail.
Formula For Probability:- There is one formula used to find out the probability of any event. The formula is the ratio of favorable outcomes and the total number of outcomes.
Probability of event to happen P(E) = a several favorable outcomes /number of total outcomes.
For example:- There are six balls in a bag, three are red, two are black and one is white. What is the probability of picking the black ball?
- Ans:- The formula here used is the favorable outcomes divided by the total number of outcomes.
I.e.. 2/6 and the exact answer are ⅓.
Types Of Probability:- There are crucial three types of probability.
- Theoretical probability:- This type is based on the possibility of anything that can happen. This probability is based on the reasons behind any possible outcome.
- Experimental probability:- This type of probability is based on the observation done during any experiment. It can be calculated based on the number of possible outcomes by the number of trials done.
- Axiomatic probability:- Under this there is a set rule that applies to all the things. With this kind of approach chances of occurrence and non-occurrence of events can be quantified.
Conditional probability is the chance of an outcome based on the occurrence of the previous year and outcome.
Equally Likely Events:- When the events have the same chance of happening then they are described as equally likely events. The results of sample space are equally Likely events if they have the same probability of occurring. Let’s study with the help of an example.
If you throw a dice then the probability of getting 1,2,3,4,5, and 6 have equal probability. Like getting 3 or 5 on dice, getting any odd or even number all these have equal probability of happening of an event.
There are many theorems in probability topics but the crucial theorems we are going to study today is Bayes theorem. This theorem finds the probability of any event but on certain conditions. It can also be described as conditional probability. Let’s understand it more precisely with the help of natural examples. Suppose we have to find the probability of choosing the green shirt from the third bag out of three different bags that have three different shirt colors. In these types of cases, the probability of certain events happening depends on the conditions of others.
Bayes theorem has many other theorems in it and one of its theorems is a bayesian theorem.
Formula:- P(A|B)= [P(B|A).P(A)] / P(B)
where P(A) and P(B) are the probability of events A and B.
P(A|B) is the probability of event A given B
P(B|A) is the probability of event B given A
So this is the interesting and confusing topic of maths I.e.. probability. If you still face any problems while studying then you can study online. Online provides us with a great platform to gain knowledge and explore any topic.
For more details visit the site cuemath.com