1. Given a fair dice, if you have to calculate the probability of each outcome from the sample space S={1,2,3,4,5,6}, there are two ways to approach the problem. Objective probability is the probability an event will occur based on an analysis in which each measure is based on a recorded observation or a long history of collected data. In contrast, subjective probability allows the observer to gain insight by referencing things they've learned and their own experience. Please answer the following questions carefully. Write the c++ programming code in Ubuntu Terminal in the form of .CPP file for each of A and B and after running the code attach both input code and output with it.

(A) For a fair dice, what is the average value of S6 for the roll of dice? S6 is the sum of six consecutive rolls. (Use subjective probability to solve)

(2) Calculate the average obtained through MC simulations, for the different number of trials Ntrial= 10,100,500,1000. Does the average calculated through MC converge to the average calculated in 1.2? (attach Graph to show convergence).

(MD Simulation Question)