Probability: The Mathematics of Uncertainty Problem Set 81 - Part 8 Evaluation Criteria for Assignments 1. Is the solution method presented in a way that makes it easy for someone else to understand the steps in mathematical thinking involved? 2. Are the variables used in a problem defined explicitly? 3. Are diagrams. charts and/or tables included? Are they carefully and clearly labeled? 4. Is there evidence of coherent mathematical thinking? Are there connections made to material Ieamed in the course? 5. Is the solution accurate? mm 1. The following spinner is used to play a three person game. ail Player 1 scores points if the spinner lands on A. Player 2 scores points if the spinner lands on B. Player 3 scores points if the spinner lands on C. Design a scoring system for this game so that it is fair. 2. Cars at lntersection' If 50% of the cars entering each fork in the road system take the northern route, what percentage of the cars that enter the system will exit at B? Player 1 scores points if the spinner lands on A. Player 2 scores points if the spinner lands on B. Player 3 scores points if the spinner lands on C. Design a scoring system for this game so that it is fair. 2 of 2 2. Cars at Intersection* If 50% of the cars entering each fork in the road system take the northern route, what percentage of the cars that enter the system will exit at B? A B 3. When flipping a coin, what is the probability of getting exactly three heads in four tosses? Display the results in a tree diagramProbability: The Mathematics of Uncertainty Problem Set #1 Part A Evaluation Criteria for Homework Assignments 1. is the solution method presented in a way that makes it easy for someone else to understand the steps in mathematical thinking involved? 2. Are the variables used in a problem dened explicitly? 3. Are diagrams, charts and/or tables included? Are they carefully and clearly labeled? 4. is there evidence of coherent mathematical thinking?Are there connections made to material learned in the course? 5. is the solution accurate? Assignment 1. Dice Problems* Find each of the following probabilities when rolling two dice: a. rolling a sum of either 7 or 9 mm. = 27.7% b. rolling a sum greater than 5 27/36 =-75% c. rolling a 6 on exactly one die d. rolling doubles e. rolling a prime number on either or both die f. rolling a sum that is a multiple of 5 g. rolling a sum greater than 12 h. write your own question and answer it 2. Number Cubes Design two number cubes so that the sum of the cubes will certainly be greater than 6, and about 70% of the outcomes will have an even sum. a. Generate all the possible outcomes. b. Find the percentage that generate an even sum. Show your work. c. Explain how your design satises both conditions