 Hello and welcome to the session. In this session, first we shall study about the experimental probability and then we shall learn how we can make predictions with the help of given probability. We know that probability is always written in fraction and we take all equally likely outcomes. Probability of an event will be given by favorable outcomes for the happening of events divided by total number of outcomes. In flipping a coin, we have two outcomes, head or tail. So probability of head coming up will be 1 by 2. So we assume that there are 50-50 chances of coming of head or tail. Now suppose we toss a coin 100 times from above. We say that head comes 50 times and tail comes 50 times. There are 50-50 chances of coming of head or tail. But if we actually toss the coin and note the observations, then this actually head appear 50 times and tail appear 50 times and the answer is no. As it is quite possible that we get different outcomes. But as we increase the sample size, we will see that the probability of a head appearing will be nearer to 1 by 2. So if we have a very large sample like tossing a coin 5000 times, we will see that appearance of a head will be approximately equal to 1 by 2. For this we calculate experimental probability. Experimental probability is given by the number of times event actually occurs divided by total number of trials. We can determine the experimental probability by performing the number of trials of the situation and counting the number of times the event actually occurs. The experimental probability thus obtained estimate of the actual probability with which the particular event or outcome occurs. The relative frequency of the outcome, the frequency divided by the number of trials, the experimental probability of an event is its relative frequency. So we can say that experimental probability relative frequency is given by frequency of the event divided by total number of trials. Now let us take an example. Suppose a metal nut was thrust 50 times, it finished on the flat side 38 times and on the edge 12 times. Now the frequency of the nut finishing on the flat side is given as 38 and we know that the relative frequency is given by frequency of the event divided by total number of trials. So here its relative frequency would be frequency of the event that is 38 by total number of trials which is given by 50. Now we also know that frequency of the nut finishing on the edge is given by 12 so its relative frequency would be the frequency of the event that is 12 by total number of trials which is equal to 50. We can summarize the results of the experiment in the form of a table. The frequency of the nut finishing on the flat side is 38 and its relative frequency is given by 38 upon 50. Similarly the frequency of the nut finishing on the edge is given by 12 and its relative frequency is 12 upon 50. The total number of trials is 50 and its relative frequency will be 50 upon 50 which is equal to 1. Now we are going to learn how to make predictions with the help of given probability. Now suppose that the nut is thrust 6000 times, we need to find how many times will it fall on the edge. Here we can use the experimental probability to make prediction for large samples. Now we have done experiment for 50 trials and the probability it will fall on the edge was given by 12 by 50 that is for 50 trials the probability that it will fall on the edge is given by 12 upon 50. Therefore for 6000 trials we multiply this probability with 6000 so probability that nut falls on edge is given by 12 upon 50 into 6000 and it is equal to 12 into 120 which is equal to 1440. We can also find the probability that nut falls flat and it is given by we know that for 50 trials the probability that nut falls flat is given by 48 upon 50. Therefore for 6000 trials it is equal to 38 upon 50 into 6000 and therefore we get 38 into 120 which is equal to 4560. Therefore for 6000 trials probability that nut falls on edge is given by 1440 and the probability that nut falls flat is given by 4560. We can also write probabilities in decimal and percentage form. In the above example we have seen that the probability that nut will fall flat was given by 38 by 50 which can be written as 0.76. Also the probability that nut will fall on edge was given by 12 upon 50 which can be written in decimal form as 0.24. And to write these probabilities in percentage form we multiply the probabilities by 100 and we get 76 percent and 25 percent as the probabilities for nut will fall flat and nut will fall on edge respectively. This completes our session. Hope you enjoyed this session.