1. You are given Three very rare three sided 'Phoenix Coins' where each of the three sides areequally likely to reveal itself upon a toss. The 'Phoenix Coin' sides and associated valuesare as follows:Phoenix Head = 0 'Tears'Phoenix Tail = -3 'Tears'Phoenix Fire = 12 'Tears'Construct Probability Distribution Tables, Probability Distribution Graphs (using Excel) andcalculate the associated Expected Values and Standard Deviations of 'Phoenix Tears' for(Case A) tosses of Two 'Phoenix Coins' and for (Case B) tosses of Three 'Phoenix Coins'.2. How many (A) Phoenix Coin combinations; and (B) outcomes of Phoenix 'Tears' arepossible if you were to toss Ten (10) Phoenix Coins?What is the (C) Expected Value of Phoenix 'Tears' if you were to toss Fourty (40) PhoenixCoins?

Given three very rare three-sided 'Phoenix Coins' where each of the three sides are equally likely to reveal itself upon a toss. The 'Phoenix Coin' sides and associated values are as follows:Phoenix Head = 0 'Tears'Phoenix Tail = -3 'Tears'Phoenix Fire = 12 'Tears'1. Tossess of Two 'Phoenix Coins':The probability of each of the three sides to reveal itself upon a tossLet's denote Phoenix Head as , Phoenix Tail as , and Phoenix Fire as .The possible outcomes tosses of Two 'Phoenix Coins' and their associated probabilities:OutcomeValue ('Tears')ProbabilityHHHTHFTHTTTFFHFTFFThe Probability Distribution Table isValue ('Tears')Probability-6-3091224The probability Distribution Graphs:The steps for Scatter Diagram in EXCEL :Step 1 : Upload the data into EXCELStep 2 : Select Insert in Home barStep 3 : Select Charts - Scatter tab in Insert barStep 4 : Click OKThe expected value, The variance, The standard deviation, -60.1111-0.66674-30.2222-0.6667200.11110.0000090.22222.000018120.22222.666732240.11112.6667646120The associated Expected Values, The Standard Deviation, Tossess of Three 'Phoenix Coins':The possible outcomes tosses of Two 'Phoenix Coins' and their associated probabilities:OutcomeValue ('Tears')ProbabilityHHHHHTHTHTHHHHFHFHFHHHTFHFTTHFFHTTFHFTHFFFFFHFHFHFFFFTFTFTFFTTTTTHTHTHTTTTFTFTFTTThe Probability Distribution Table isValue ('Tears')Probability-9-6-306912212436The probability Distribution Graphs: -90.037037-0.333333-60.111111-0.666674-30.111111-0.33333100.0370370060.1111110.666667490.222222218120.1111111.33333316210.1111112.33333349240.1111112.66666764360.0370371.33333348The associated Expected Values, The Standard Deviation, 2. Consider the case of tossing Ten (10) Phoenix CoinsThe number of possible combinations for tossing Phoenix Coins with sides each is given by .(A) In this case, since each Phoenix Coin has 3 sides, and you are tossing 10 coins:The number of Phoenix Coin combinations(B) The general formula for finding the number of ways successes can occur in trials is given by: The number of times Phoenix 'Tears' are possible if you were to toss Ten (10) Phoenix Coinswhere is the number of times 'Tears' appears.(C) The Expected Value of Phoenix 'Tears' if you were to toss single Phoenix Coins.The Expected Value of Phoenix 'Tears' if you were to toss forty (40) Phoenix Coins1. Tossess of Two 'Phoenix Coins':The Probability Distribution Table isValue ('Tears')Probability-6-3091224The probability Distribution Graphs:The associated Expected Values of 'Phoenix Tears' is 6The Standard Deviations of 'Phoenix Tears' is 9.1652Tossess of Three 'Phoenix Coins':The probability distribution table isValue ('Tears')Probability-9-6-306912212436The probability Distribution Graphs:The associated Expected Values of 'Phoenix Tears' is 9The Standard Deviations of 'Phoenix Tears' is 11.2252. (A) The number of Phoenix Coin combinations(B) The number of times Phoenix 'Tears' are possible if you were to toss Ten (10) Phoenix Coins(C) The Expected Value of Phoenix 'Tears' if you were to toss forty (40) Phoenix Coins