All, I need someone who is very good with statistics and probability to help on this...

Question 1.2 (2 points) Complete the sample space below with possible game outcomes S = {WWW, WLL, LWL, ... .., LLL} Question 1.2 answer here Question 1.3 (4 points) . a) How many permutations in the sample space represent 3 loosing dice (3 dice not equal to the number you picked)? . b) How many permutations in the sample space represent 2 loosing dice and 1 winning dice (2 dice not equal to the number you picked, 1 dice equal to the number you picked)? . c) How many permutations in the sample space represent 1 loosing dice and 2 winning dice (1 dice not equal to the number you picked, 2 dice equal to the number you picked)? . d) How many permutations in the sample space represent 3 winning dice (3 dice equal to the number you picked)? Question 1.3 answer here a) Question 1.4 (5 points) Given your answer to question 1.3 and the binomial probability formula: (") p(W)* p(L)"- . a) What is the probability to throw 3 loosing dice (3 dice not equal to the number you picked)? b) What is the probability to throw 2 loosing dice and 1 winning dice (2 dice not equal to the number you picked, 1 dice equal to the number you picked)? c) What is the probability to throw 1 loosing dice and 2 winning dice (1 dice not equal to the number you picked, 2 dice equal to the number you picked)? d) What is the probability to throw 3 winning dice (3 dice equal to the number you picked)? e) Verify that all these probabilities sum to 100%Question 1.5 (4 points) Calculate the expected winnings for this game. Remember, expected value equals the weighted sum of all possible outcomes, where the weights equal the outcome probabilities: E(X) = Ex xP(X = x) Question 1.5 answer here. Remember to show your calculation Game simulation In this section we are going to simulate this game and compare the simulated winnings against our analytical-expected-winnings-calculation-result that we covered in question 1.5 We have seen many times that we can draw heads or tails using uniform(0, 1) draws by allocating heads if U(0, 1)