 Hi and welcome to the session. I'm Shashin and I'm going to help you with the following question. Question says, the mean of the numbers obtained on throwing a die having written 1 on 3 faces, 2 on 2 faces and 5 on 1 face is we have to choose the correct answer from A, B, C and D. Let us now start with the solution. First of all, let us assume that X denote the number on the face of the die. We know die has 6 faces in all and we are given that 3 faces have 1 written on them, 2 faces of the die have 2 written on them and only 1 face of the die has 5 written on it. So we can write X is a random variable which can assume values 1, 2, 5. We know in a single throw of a die we will get either 1 or 2 or 5. So random variable X can assume values 1, 2, 5. Now we will write the probability distribution of random variable X. We know random variable X can assume values 1, 2, 5. Now probability of getting 1 in a single throw of die is equal to 3 upon 6 which is further equal to 1 upon 2. We know 1 is written on 3 faces of the die and total faces of the die is equal to 6. So probability of getting 1 in a single throw of die is equal to 3 upon 6 which is further equal to 1 upon 2. Similarly probability of getting 2 in a single throw of die is equal to 2 upon 6. We know outcome say variable 2 in a single throw of a die is equal to 2 and total possible outcomes is equal to 6. So probability of getting 2 in a single throw of die is equal to 2 upon 6 which is further equal to 1 upon 3. Now probability of getting 5 in a single throw of die is equal to 1 upon 6. We know total possible outcomes, variable 2, 5 is equal to 1 and total number of possible outcomes in a single throw of die is equal to 6. So probability of getting 5 in a single throw of die is equal to 1 upon 6. Now we have to find the mean of random variable X. We know we represent mean by EX which is further equal to summation Xi Pi where I is equal to 1 to N. Now this value represents X1, this represents X2, this represents X3. This value represents P1, this value represents P2 and this value represents P3. So mean is equal to X1 P1 plus X2 P2 plus X3 P3. Now we will substitute corresponding values of X1, X2, X3 and P1, P2, P3 in right hand side of this expression and we get 1 multiplied by 1 upon 2 plus 2 multiplied by 1 upon 3 plus 5 multiplied by 1 upon 6. Now 1 multiplied by 1 upon 2 is equal to 1 upon 2, 2 multiplied by 1 upon 3 is equal to 2 upon 3 and 5 multiplied by 1 upon 6 is equal to 5 upon 6. Now adding these three terms by taking their LCM we get 3 plus 4 plus 5 upon 6. Now this is further equal to 12 upon 6. Now we will cancel common factor 6 from numerator and denominator both and we get mean of random variable X is equal to 2. Now we get the mean of the numbers obtained on throwing a die having written 1 on 3 faces, 2 on 2 faces and 5 on 1 face is 2. So our correct answer is B. So this is our required answer. This completes the session. Hope you understood the solution. Take care and have a nice day.