# Introduction to Probability

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## Lecture description

This video will give you an overall idea on how to solve a problem based on probability.

The video shows how to understand a question and how to go about finding the solution. If you are beginner then this video will really help you in tackling problems related to probability in a better manner.

### Learn more from the full course

Probability for beginners | Mathematics & StatisticsAn entire course on Statistics and Probability from beginner's level to advanced level.

02:21:03 of on-demand video • Updated August 2019

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Hi friends. This is a common sight nowadays. How do you think the application predicts the next possible route. The application has about half a million words in English Dictionary stored as part of its database. Then scores ghostly words which we use very often high of these scores more. The chances of the use of the word and so he would is suggested. In fact it also scores phrases so that it can suggest the words which are used together. For example if you wish your friends on the board D by texting wishing you a very happy birthday and a wonderful year ahead. Every time you write happy the next words suggested would be to Buddy new with the word with the highest score is pleased in the center of the application. Thus this suggestion by calculating the chances or the probability of using a word depending on the score of the would the chance of happening often even when expressed in terms of numbers is probability. Let's look at some simpler examples to understand what is the science behind the prediction. Some of the items used and how do we calculate the chances of the happening often even. Suppose we want to start a game of noodle with a friend and to decide who goes first. We toss a coin. The person getting a head would start the game. One stars there can be two results. Either we get ahead but deal. These results are called outcome in mathematics. Tossing a coin is called an experiment or a trial. It is an action which can have more than one result an outcome is abrupt and results. When the experiment or trial is performed right if we collect all the outcomes of an experiment together it will look like a set. We have already learnt about sets in our previous greed. In the case of tossing of a coin it would look like this in probability. All the possible outcomes of an experiment is gone. The sample space. So can you tell me what would be the sample space when a dice is wrong. The action here is rolling of the dice so it is called a trial. When the dice is roll we could get one two three and so on till six. These are the possible results are the outcomes. So the sample space here would be D set S when and dinosaurs rule a desired result could be something like getting a 6. That is just the outcome 6 in these ample space are getting an even number which will have the even numbers from the sample space that is 2 4 and 6. Set or collection which has the desired outcomes is called an even to calculate a probability correctly. It is very essential that we write a sample space correct. So far we have seen two parts. First one is the prediction of the. Why messaging and tossing of a coin or rolling a die dummy friends. Are you able to connect with it. Let's discuss at least by now. If one would ask you what is the chance of getting ahead when a coin is tossed. You would simply say 50 percent right. But if I did to you when I toss this coin 100 times I got head as an outcome 85 times. Will you still see that there is a 50 percent chance of getting ahead. No. So friends basically there are two types of probability experiment 2 and theoretical and for the same even the answer can be different. So let's see an example and then we'll solve a question. Suppose team E. and Team B. Well to play a game of cricket at the beginning of the match. If we were to predict the winners of the match when we know nothing about their earlier performances we would see they both have 50/50 chance of winning. This is called theoretical probability. Suppose in the past they've played 10 matches off which team E has won eight of them. Then on being us to predict the winners we would see Team 8. This prediction or calculation of probability based on some data is called emphatically probability. Now I hope there is no confusion about empirical and theoretical probability in this session. We should learn only how to calculate empirical probability empirical on experimental probability is the ratio of the number of times and even occurs to the total number of times the experiment is performed. We call it empirical as a probability B Calculate is going to be based on the results of an experiment that was performed in a game of Ludo. We don't want the dice here. The list of possible outcomes was so the sample space was suppose by the end of the game the dice was rolled five hundred times and the observations were recorded as what is the probability that when the dice was rolled for was on top the result was an art number no no. The try is rolling off a dice. The number of trials is five hundred. They're designed even is getting hopeful. So using the formula for empirical probability probability of getting a forward is ninety four upon five hundred odd for the second but the desired even is getting an odd number of all the outcomes in the sample space. The art numbers are 1 3 and 5 so the probability of getting an odd number is ninety six plus 70 plus seventy five upon five hundred or 241 upon five hundred or. What does the probability of getting a zero hold now zero is not a part of the sample space. So now applying the formula we get probability of getting a zero is you'd remember tossing a coin at the start of the game. What if the coin is caused one hundred times and the results are. Forty seven times fifty three times what does the probability of getting ahead and that of getting a deal. Yo so probability of getting ahead is forty seven upon one hundred or. Also probability of getting a deal is fifty three upon one hundred or notice here that probability of getting ahead plus probability of getting a deal. When added together it gives us 1 also probability of any event is always greater than zero or equal to zero and less than one or equal to one. Now a few facts about probability weakened state of the probability of an even lies between 0 and 1 the sum of probabilities of all possible outcomes is one the probability often even that is not in the sample space is zero with the learnings from this session trying solving this question. If you have any doubts why in solving the question please feel free to comment on the video or call us or WhatsApp us. If you have like this session please hit the Like button and don't forget to subscribe to watch on them. Hit the ball like you and never miss another update from let's do it. Keep watching. Keep learning. Thank you.