Question Number (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. (A) Monte Carlo simulations belong to which set of probability estimates? Objective or Subjective? (B) 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) (C) Write a short program 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) (D) 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)

(Molecular Dynamics Simulation Question. Ubuntu Terminal Software)