### Monte Carlo Method Simulation for Dice Probability#### Objective:Use the Monte Carlo method to simulate the roll of two dice. Find the probability of the sum of the faces to be 6 or less.#### Procedure:The following table represents 10 trials conducted using Excel to simulate the rolling of two dice.| No. | Dice 1 | Dice 2 | Total ||-----|--------|--------|-------|| 1 | 3 | 4 | 7 || 2 | 3 | 2 | 5 (0.067) || 3 | 5 | 1 | 6 (0.08) || 4 | 5 | 6 | 11 || 5 | 1 | 5 | 6 (0.08) || 6 | 6 | 3 | 9 || 7 | 2 | 3 | 5 (0.067) || 8 | 6 | 4 | 10 || 9 | 1 | 6 | 7 || 10 | 4 | 5 | 9 |### Explanation: 1. **Dice Rolls**: Two dice are rolled, and their face values are recorded in the columns 'Dice 1' and 'Dice 2'.2. **Sum Calculation**: The total sum of the values from 'Dice 1' and 'Dice 2' is calculated and recorded in the 'Total' column.3. **Probability Calculation**: The numbers in parentheses (e.g., 0.067, 0.08) denote the probability of obtaining a sum of 6 or less for that particular roll.#### Analyzing the Results:- **Trial Analysis**: Across the 10 trials, sums less than or equal to 6 appear in trials 2, 3, 5, and 7.- **Probability Derivation**: The probabilities next to each result show the likelihood of those sums occurring as calculated from the specific trial.This simulation aims to provide an empirical probability which can be compared with theoretical results, validating the Monte Carlo method.

Monte Carlo output is given for rolling two dices. N=10 Formula, Probability = Favorable outcomes…

Answered: Q.3 Use Monte Carlo method to simulate…

A First Course in Probability (10th Edition)

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Chapter1: Combinatorial Analysis

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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Q.3 Use Monte Carlo method to simulate the roll of two dices. Find the probability of the sum of two faces to be 6 or less. The following table give 10 trials by using excel. Dice 2 NO. Dice 1 3 4 Total 7 +50-67 3 2 2 1 5 6 008 3 5 6 11 1 5 6 5 oved 6 6 3 9 7 2 3 5 01667 8 6 10 4 1 6 7 4 9 5 9 10