 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that use a table to illustrate the sample space when two unbiased die are wrote simultaneously. What is the probability of getting a doublet? We know that sample space is a complete list of all possible outcomes of a random experiment. This is also known as possibility space and is denoted by capital S. We also know that a doublet means when the numbers appearing on both the die are same and we know that probability of an event is given by favorable outcomes upon total outcomes with this T-ideal. Let us proceed to the solution. Now in this question we need to find the sample space when two unbiased die are wrote simultaneously. Also we need to find the probability of getting a doublet. So here we will use table to write sample space of outcomes when two die are wrote simultaneously. We know that numbers from one to six are written on the sites of a die. So possible outcomes of first dies is equal to the set containing elements 1, 2, 3, 4, 5 and 6. Similarly possible outcomes for second dies is equal to the set containing elements 1, 2, 3, 4, 5 and 6. Let us draw a table for the outcomes. The rows represent the outcomes for the first dies and the columns will represent the outcomes for the second dies. Here we see that the rows represent the outcomes for the first dies and the columns represent the outcomes for the second dies. And we have written the combination in the table cells corresponding to respective row and column element. That is if we get 1 on the first dies and 1 on the second dies we will get the combination as 1, 1. Similarly if we get 1 on the first dies and 2 on the second dies then our combination will be 1, 2. Similarly if we get 2 on the first dies and 1 on the second dies we will get the combination as 2, 1 and in this way we get all the possible combinations. And this is the required sample space for 2 dies in the form of a table. And there are 36 possible outcomes in the sample space. Now we need to find the probability of getting a doublet and from the key idea we know that a doublet is when the numbers appearing on both the dies are same. So let event A be equal to getting a doublet which means getting same number on both the dies and from the sample space we can see that there are 6 outcomes in favor of event A that is 1, 1, 2, 2, 3, 3, 4, 4. 5, 5 and 6, 6. So we can say there are 6 outcomes in favor of event A and from the key idea we also know that probability of an event is given by favorable outcomes by total outcomes. Therefore probability of event A will be equal to favorable outcomes by total outcomes we know that there are 6 outcomes in favor of event A. So number of favorable outcomes would be 6 and total outcomes would be given by 36 as there are 36 possible outcomes in the sample space. In this case we say that probability of event A is given by 1 upon 6 thus probability of getting a doublet is equal to 1 upon 6 which will be required answer this completes our session hope you enjoyed this session.