 Hello everyone. Welcome to this session. Today we want to go introduction to probability. I am Mr Praveen Kumar. The learning outcome of this session is at the end of this session student will be able to explain the concept of probability. The contents of this session are Experiments, Outcomes, Samples, Space, Assigning Probabilities, Events and their Probabilities, Basic Relationships of Probability and Addiction Law. Now we want to see one by one. The first one is Experiments, Outcomes, Samples, Space. Here we taken an example of tossing a coin that is an experiment of a tossing of a coin. Now output of this tossing of a coin is basically head or tail. This head or tail is included in this sample space. That experiment outcomes that is head or tail this is in a sample or it is also called as sample points. This sample points included in the sample space. Next Assigning Probabilities. Probabilities can be defined in three ways. First, Classical Method. Second, Relative Frequency Method. Third, Subjective Method. First, Classical Method. Classical Method means Assigning Probabilities based on the assumption of equally likely outcomes. Examples of Classical Probability would be Fair Dice Roll. When we Fair Dice Roll there are possible outcomes or six because there are six phases. It is equally probable that it will any of the six numbers on the dice that is 1, 2, 3, 4, 5 or 6. That is Classical Method Probability it will come in between 0 to 1. Second one is Relative Frequency Method. Relative Frequency Method means Assigning Probabilities based on experimentation or historical data. For example, historical data we taken as colors. Here purple, blue, pink and orange there are four colors. Now Relative Frequency is definition is purely based on this historical data. Now frequency of this purple color is 7. The frequency of this blue color is 3. The frequency of the pink color is 5 and the frequency of orange color is 5. Therefore total frequency become of this color 7 plus 3 plus 5 plus 5 is equal to 20. Now Relative Frequency we want to calculate for each color. For example, now first we calculate the Relative Frequency for purple color. The Relative Frequency definition is equal to frequency divided by total number of frequency outcome. Therefore apply that definition to this Relative Frequency of purple color. The Relative Frequency equal to 7 by 20 is equal to 35%. The same formula is applied for the blue colors. For the Relative Frequency for this blue color equal to total number of frequency 3 divided by 20 that is 15%. For the pink color for the Relative Frequency is 5 by 20 that is 25%. For the orange color it is 5 by 20 is equal to 25%. Now the basic formula of the probability apply to this Relative Frequency method that the 35% plus 15% plus 25% plus 25% become 100%. Means this overall relative probability is 100%. Means this always range is lies between 0 to 1. Next definition method is subjective method. Assigning probabilities based on the judgment. Here for the subjective method we apply only judgment. Judgment means individual personal judgment it is not on purely mathematical calculation. But always remember the probabilities always lies between 0 to 1. Whenever we apply their judgment not a mathematical calculation then also we require the answer is 0 to 1. For example of the subjective method is to locate water petroleum or minerals lying underground are employed to predict the probability of existence of the required material. For example whether there is a water present or petroleum present or mineral present. If that probability indicates 0 means there is nothing. If there is indicate 1 means there is a possibility of water petroleum or minerals. Now next topic is events and their probabilities. First we see the definition of events. Events and event is a collection of sample points. It is a collection of sample points means for example tossing a coin it see there are two possibly outcomes one is a head or tail that is the events are head and tail that is a total number of events. The probability of any event is equal to the sum of the probabilities of the sample points in the event means the outcome of this tossing a coin is head or tail the summation of these two becomes the events of that probabilities. Basic relationships of probability there are basically three relationships of the probability first complement of an event second intersection of two events and third one is mutually exclusive events. These three relationships of the probability we see one by one with the help of diagrams first complement of an event. This figure two shows the complement of two events. Now here event a shows event a and the complement of this event is shown by a c means what a c shows the complement of event a means what it does not contain the part of event a that is called as a complement of an event a. Now for example suppose in that event a contains our one then complement of a c is zero next intersection of two events this diagram shows intersection of a two events that is a and b this this mathematically indicated by a intersection b these two events event a and event b the intersection of these two events and b means they are having a some common elements this is a shown with the help of this diagram. Now next last one is mutually exclusive events the mutually exclusive events diagram is shown here the mutually exclusive events it requires two events that is event a and event b this event a and b is called as mutually exclusive events means they have a no common elements if you observe in this diagram event a and event b are separate events and they have a no common elements that is called as mutually exclusive events. Now we want to study addition laws addition law is probability of a union b is equal to probability of a plus probability of b minus probability of a intersection b this addition law is derived for the two events that is event a and b this can be addition law derived for you know n number of events here we want to study for only two numbers of events that is this one now mutually exclusive events apply this mutually exclusive events to this addition law now after applying this mutually exclusive events to this above equation the above equation become as probability of a union b is equal to probability of a plus probability of b because for the mutually exclusive event probability of a intersection b become as a zero therefore therefore the mutually exclusive events the addition law become as probability of a union b is equal to probability of a plus probability of b this one we use for the mathematical calculations now references for this session is thank you