Please use the MDM4U (Grade 12 Data Management course in Ontario, Canada) methods to answer the following questions. Please do not AI or ChatGPT this; I need to know how to do it. Make sure the methods relate to unit 3: Discrete Probability Distributions. Show all necessary steps.

6. Two coins are randomly drawn, one after another (no replacement), from three quarters, a loonie, and two toonies.

a) Illustrate the probability distribution. You can use a table, tree diagram, etc. [4]

b) Determine the expected amount of money that would be drawn. [2]

Question 6 You are drawing 2 coins at random, without replacement, from: + 3 quarters = Q = $0.25 $1.00 = $2.00 * 1 loonie * 2 toonie Goal: a) Create a probability distribution of the total value of 2 coins. +) Find the expected value (mean) of the money drawn, * Part (a): Create the Probability Distribution + Step 1: Count the Total Number of Ordered Outcomes You are choosing 2 coins in order, without replacement, Total number of ways to draw 2 coins from 6: + Step 2: List All Possible Outcomes and Their Values Let's go through all combinations of ordered draws and calculate their total values. We will label the quarters as Q1, 02, 03 One loonie = L Toonies = 71, 12 Possible pairs and their values: First Coin Second Coin Value a a2 0.50 a 3 0.50 a2 L 1.25 a2 1 2.25 a2 12 2.25 93 a 0.50 a3 a2 0.50 93 L 1.25 3 a 2.25 93 T2 2.25 L a 1.25 L a 1.25 L 3 1.25 t 1 3.00 L 12 3.00 n a 2.25 n a2 2.25 n 3 2.25 1 L 3.00 1 12 4.00 2 a 2.25 2 a2 2.25 12 3 2.25 2 L 3,00 2 1 4.00 + Step 3: Group Outcomes by Total Value Now we count how many times each total value appears among the 30 outcomes: Total Value ($) How Many Times? 0.50 6 times (9+0) 1.25 6 times (Q+4 or L+Q) 228 T2times (QT oF T+Q) 3.00 Atimes (L#T or T#L) 4.00 2 times (T+7) Final Probability Distribution Table: Total Value of 2 Probability Coins ($) 0.50 0.20 1.28 0.20 2.25 0.40 3.00 0.133 4.00 0.067 * Part (b): Find the Expected Value 'The expected value is the mean of the distribution, Use this formula: E(X) = Y(e- Plz) Now substitute values from the table: E(X) =0.10 + 0.25 + 0.90 + 0.399 + 0.268 E(X) ~ 1.917 + a) Probability Distribution: inal Answer: Total Value of 2 Probal Coins ($) 0.50 0.20 1.25 0.20 2.28 0.40 3.00 0.133 4.00 0.067 + b) Expected Value: EX) = S192 ~S eS mayan. wranny Coins Without Replacement From: 3 Quarters (Q1, Q2, Q3), 1 Loonie (U), 2 Toonies (T1, T2) LEVEL 1 - First Coin Draw You have 6 possible first draws: Qi Q2 +93 eft m1 72 For each of these, the second draw has 5 remaining coins. * Start with Q1 as first draw: *Q1 = Q2=0.25 + 0.25 = 0.50 Q1 = Q3=0.25 + 0.25 = 0.50 Q1 => L =0.25+1.00 = 1.25 *Q1 | 71=0.25+ 2.00 = 2.25 *Q1 = T2=0.25 + 2.00 = 2.25 *Q2 |= Q1=0.25+0.25 = 0.50 * Q2 = Q3=0.25 + 0.25 = 0.50 Q2L =0.25+1.00=1.25 *Q2 | 71=0.25+ 2.00 = 2.25 *Q2 = 72=0.25+ 2.00 = 2.25 * Q3 as first draw: *Q3 = Q1=0.25+0.25 = 0.50 * Q3 = Q2=0.25+0.25 = 0.50 Q3 = L =0.25+1.00 = 1.25 *Q3 = 71 =0.25+ 2.00 = 2.25 Q3 = T2=0.25+ 2.00 =2.25 * L (Loonie) as first draw: *L = Q1=1.00 + 0.25 = 1.25 *L Q2=1.00 + 0.25 = 1.25 *L | Q3=1.00 + 0.25 = 1.25 *L = 7T1=1.00 + 2.00 = 3.00 *L = T2=1.00 + 2.00 = 3.00 T1 as first draw: *T1 =| Q1=2.00+ 0.25 = 2.25 T1 = Q2=2.00+0.25 = 2.25 T1 = Q3=2.00+ 0.25 = 2.25 T1 = L =2.00 + 1.00 = 3.00 *T1 = T2 = 2.00 + 2.00 = 4.00 72 as first draw: * 72 = Q1=2.00+0.25 = 2.25 * 72 = Q2=2.00+0.25 = 2.25 * 72 = Q3=2.00+0.25 = 2.25 * 72 = L =2.00 + 1.00 = 3.00 * 72 = T1 = 2.00 + 2.00 = 4.00 (J Summary of All Totals Total Value Occurrences $0.50 6 $1.25 6 $2.25 12 $3.00 4 $4.00 2 Total Outcomes: 6 x 5 = 30 (Confirmed)