 Hello and welcome to the session. The given question says, a pair of dice is tossed twice if the random variable x is defined as the number of doublets, find the probability distribution of x. Let us now start with the solution and here we are given that x is equal to the number of doublets which appear when a pair of dice is tossed twice. Now the possible doublets are 1, 1, 2, 2 that is on both the dice the same number appears. So these are the doublets clearly since here that a pair of dice is tossed twice therefore x can take the value 0, 1 or 2 that when pair of dice then the total number of possible outcomes is equal to 36 and out of these 36 possible outcomes 6 are doublets therefore probability of getting a doublet is equal to the number of favorable outcomes of getting a doublet divided by the total number of possible outcomes and the favorable are 6 and the total number of outcomes are 36 so probability of getting a doublet is 1 by 6. Therefore probability of not getting a doublet is equal to 1 minus 1 by 6 which is equal to 5 by 6. Now let us find the probability when x is equal to 0 that is probability of no doublet and here the pair of dice is 5 divided by 6. This is the probability for the first row and for the second row and this is equal to 25 divided by 36. Now let us find probability at x is equal to 1 that is probability of 1 doublet 1 no doublet sorry non doublet and this is equal to doublet non doublet in the second row non doublet in the first probability of a doublet in the second row probability of a doublet values probability of getting a doublet is 1 by 6 into probability of getting a non doublet does into 1 by 6 is equal to 10 divided by 36 and cancelling 25 to 10 2 into 18 is 36 so we have 5 divided by 18. So probability when x is equal to 1 is 5 divided by 18 that is probability of getting 1 doublet in 2 tosses is 5 divided by 18 that is probability that probability of doublet into probability of doublet that is 1 by 6 into 1 by 6 is equal to 1 divided by 36 therefore we have probability at x is equal to 2 is equal to 1 by 36 the required distribution to show the probability distribution in the first row we shall write the values of x and the second they have probabilities and take the values 0 1 and 2 and the probability when x is equal to 0 is 25 divided by 36 probability when x is equal to 1 is 5 divided by 18 and probability when x is equal to 2 is 1 divided by 36. So this completes the session by and take care.