 Hello and welcome to the session. In this session we will learn about probability. Probability is the likelihood or chance that something is the case or will happen. Before discussing about the theoretical probability of an event E, first let's discuss what are equally likely outcomes. The outcomes of a random experiment are said to be equally likely if each one of them have equal chance of occurrence. Like for example if we toss a coin we will get either head or tail. In this case we can easily see that each outcome that is head or tail has equal chance of occurrence. Thus we say that the outcomes head or tail are equally likely outcomes. Let's consider an event E. Now the theoretical probability of an event E which is also given by PE would be equal to number of outcomes favorable to E upon number of all possible outcomes of the experiment. Where the outcomes of the experiment are assumed to be equally likely. Theoretical probabilities also referred as probability. Let's consider an example in which the coin is tossed once and we have to find the probability of getting a head. Here the event E is taken as getting a head then probability of the event E that is probability of getting a head would be equal to number of outcomes favorable to E that is when we toss a coin we get a head or a tail. So chances of getting a head is 1 so number of outcomes favorable to E is 1 upon number of all possible outcomes all possible outcomes of this experiment would be 2 that is head or a tail. So 1 upon 2 is the probability of getting a head. An event which is sure or certain to occur is called the sure event or a certain event. Now the probability of a sure event or you can also say certain event is 1. When we throw a die the sample space for this experiment would be this. Now let E1 be the event of getting number less than 7. Clearly you can see that each outcome of this experiment is a number less than 7. So the number of favorable outcomes is the same as the number of all possible outcomes which is 6. So probability of this event would be 6 upon 6 that is 1 and E1 is a sure event. An event which is impossible to occur is called an impossible event. Now the probability of an impossible event is 0. Now again we consider that we throw a die. Now the sample space for this experiment would be this. We consider an event E1 of getting number 8 in this sample space as you can see there is no number 8. So probability of this event would be equal to 0 upon the total number of outcomes that is 6 and so its probability is equal to 0. So this is an impossible event. Next we have that from the definition of the probability pevc that the numerator is always less than or equal to the denominator. So the probability of an event E is a number such that this number pe that is probability of the event E is greater than equal to 0 and less than equal to 1. That is for any event E its probability would be between 0 and 1 and it can also be equal to 0 or 1. Next point that we discuss is an event having only one outcome is called an elementary event like if we toss a coin the events that would occur would be let it be event E of getting a head and event F of getting a tail. As you can see both these events event E and event F have only one outcome so they can be considered as elementary events and also we have some of the probabilities of all the elementary events of an experiment is like in this above example when we toss the coin we see that probability of getting a head that is probability of E would be equal to 1 upon 2 and also probability of getting a tail that is probability of F is equal to 1 upon 2. And both the events E and F are the elementary events so some of the probabilities of all elementary events of this experiment that is probability of E plus probability of F would be equal to 1. Now for any event E probability of event E plus probability of E bar is equal to 1 where this E bar stands for not E and these events E and E bar are called the complementary events in general we can also say that probability of E bar is equal to 1 minus probability of E. Again consider the example when we toss a coin there are two possible outcomes head and tail let E be the event of getting a head then the event E bar which is the complement of the event E is an event of getting a tail. Now probability of getting a head that is probability of event E is 1 upon 2 and probability of event E bar that is probability of not getting a head is also 1 upon 2 and as you can see the probability of E plus probability of E bar is equal to 1. Thus the events E of getting a head and E bar of getting a tail are complementary events. This completes the session hope you understood the concept of probability.