Three dice are tossed, one red, one blue, and one green. a. What is the probability that the sum of the three faces showing equals 7? b. Write an R program that simulates this random experiment 106 times and calculates the proportion of simulations in which the sum of the three faces showing is 7. Include the program and its output in your homework submission. Hint 1: By the Law of Large Numbers, the number you find should be close to the theoretical probability found in question 1. Hint 2: In your R program, you can use a 'for' loop to repeat the simulation 106 times (each time, simulate the 3 dice roll and store their sum; at the end, find the proportion of 7's out of all results). A faster method is to simulate a dice roll 3x10 times, arrange this vector into a matrix with 3 rows and 106 columns (or the other way around), calculate the column sums of the matrix, and finally determine the proportion of 7's among these sums