 Hi and welcome to the session. I am Shashi and I am going to help you with the following question. Question says, suppose that two cards are drawn at random from a deck of cards. Let X be the number of faces obtained. Then the value of mean of variable X is, we have to choose the correct answer from A, B, C and D. Let us now start with the solution. Now first of all let us assume that X denotes the number of faces obtained. So we can write let X denote the number of faces obtained. Now we know two cards are drawn. Now three cases are possible when two cards are drawn. First case is both cards are races. Second case is one card is A's. Third is none of the cards is A's. Now we can say the random variable X can assume values 0, 1 or 2. Now we will write the probability distribution of variable X. We know random variable X can assume values 0, 1 or 2. Now first of all we will find probability of getting 0 A's. It is equal to 48 upon 52 multiplied by 48 upon 52 where cards are drawn with replacement. We know number of faces in a deck of cards is equal to 4 and total number of cards in a deck of cards is equal to 52. Now outcomes favourable to 0 A's is equal to 48 that is 52 minus 4 and total number of possible outcomes is equal to 52. So this is the probability of drawing first card. Similarly this is the probability of drawing second card. Remember that here cards are drawn with replacement. Now simplifying further we get probability of getting 0 A's is equal to 144 upon 169. So here we can write 144 upon 169. Now we will find the probability of getting single A's. It is equal to 4 upon 52 multiplied by 48 upon 52 plus 48 upon 52 multiplied by 4 upon 52. Now clearly we can see this is the probability of drawing first card that is A's and this is the probability of drawing second card which is other than A's. So probability of drawing second card is 48 upon 52. It may happen that first card is A's and second card is other than A's. It may happen that second card is A's and first card is other than A's. So we will add both of these probabilities. So we can write probability of getting single A's is equal to 4 upon 52 multiplied by 48 upon 52 multiplied by 2. Simplifying further we get it is equal to 24 upon 169. So we can write probability of getting a single A's is equal to 24 upon 169. Now we will find probability of getting 2 A's's. It is equal to 4 upon 52 multiplied by 4 upon 52. We know total number of outcomes favourable to A's is equal to 4 and total number of possible outcomes is equal to 52. So probability of drawing first card is 4 upon 52. Similarly probability of drawing second card is also 4 upon 52. Since cards are drawn with replacement so probability of both the cards is 4 upon 52. Now simplifying further we get probability of getting 2 A's is equal to 1 upon 169. Now here we can write 1 upon 169. Now we know mean of random variable X is equal to Ex which is equal to summation of Xi Pxi where i is equal to 1 to n. Now we will find X1 P1 plus X2 P2 plus X3 P3. Now we can write 0 multiplied by 144 upon 169 plus 1 multiplied by 24 upon 169 plus 2 multiplied by 1 upon 169. Now simplifying further we get 24 upon 169 plus 2 upon 169 which is further equal to 26 upon 169. This term will become 0 and 1 multiplied by 24 upon 169 is 24 upon 169 only. Similarly multiplying these two terms we get 2 upon 169. Adding these two terms we get 26 upon 169. Now we will cancel common factor 13 from numerator and denominator both and we get 2 upon 13. So mean of variable X is equal to 2 upon 13. So the correct answer is D. This is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.