 Hello and welcome to the session. In this session we will discuss the non-uniform probability model. Now let us start with its illustration. Now suppose we have a die with digits 1, 2, 3, 4, 6 and 6 marked on it. Now here in total we have 6 digits. Now if we roll the die with all the numbers having equal chances of being rolled then probability that 1 appears or probability of getting a number 1 is the number of favorable outcomes which is 1 upon total number of outcomes which is 6. So this is equal to 1 upon 6 and probability of getting a number 2 is again 1 upon 6 and probability of getting the number 3 is again 1 upon 6. Then probability of getting a number 4 is 1 upon 6. Now we know that 6 is marked 2 times on the die so probability of getting a number 6 is the number of favorable outcomes which is 2 upon total number of outcomes which is 6. So this is equal to 1 upon 3. Now here one thing you can notice that 5 is not on the die. It means there is something wrong. Now we know that a fair or unwise die consists of numbers 1, 2, 3, 4, 5 and 6 and each has the probability of 1 by 6. But here 6 appears twice and has greater probability than rest of the numbers. So there are not equally likely chances of each number to appear on the die. This means it is a biased die. And when we perform an experiment when all the items do not have equally likely chances of being selected then it is called a non-uniform probability model. Now let us discuss another example. And in this example we will toss a paper cup so that it spins in the air. Now record how it lands right side up, upside down or on its side. Now let us suppose the cup is tossed 100 times. Now we have the following recordings. From these recordings we can see that the chances that the cup will fall on the side are maximum and the experimental probability of falling on its side is equal to 61 upon 100 which is equal to 0.61. Now if the chances of the three falling positions are equally likely then let us find the critical probability of falling of the cup on its side. Now here total number of outcomes is 3 and number of favorable outcome is 1. So theoretical probability of falling on its side is 1 upon 3 which is equal to 0.33. Now from the experimental probability you can see that the chances of three falling positions are not equally likely because otherwise if the chances are equally likely then expected probability of falling on its side is 0.33. So there is a discrepancy in both probabilities. Now let us suppose that Tim and Jack play a game of tossing this paper cup. Now if the cup falls on its side then Tim wins right side up then Jack wins. Now clearly we can see that chances that Tim wins are more than chances that Jack wins because we know that the chances of falling on its side are more than chances of falling right side up. So chances of winning the game for both the players are not equal. Now here also you can see that all the items do not have equally likely chances of occurrence. So it is also a non-uniform probability model. So in this session we have learnt about non-uniform probability model and this completes our session. Hope you all have enjoyed the session.