8. 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. and write the c++ programming code in Ubuntu Terminal in the form of .CPP file for each of parts B and C and after running the code attach both input code and output with it. Also attach the Monte carlo convergence graph from segregetting data from .cpp file to excel with proper steps.

(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).

(B) Write a short c++ program in the form of .cpp file in ubuntu terminal to calculate the same (S6) using Monte Carlo simulations for a fair dice (Hint: This involves generating 6 random numbers in each trial and calculating their average. I.e. Each Trial involves generating 6 random numbers).

(C) Calculate the average obtained through Monte carlo simulations, for the different number of trials Ntrial= 10,100,500,1000. Does the average calculated through Monte carlo converge to the average calculated in part (A)? (attach Graph to show convergence).

(Molecular dynamics simulation Question)