(Solved): This Quiz Is Over The Following Topics: Probability (Ch 7) Conditional Probability (Ch7) Law Of Large Numbers (Ch7)

QUESTION 1 Scenario: You and your spouse are arguing over who gets to pick the TV show to watch tonight. As a game to settle this argument, you each choose a game to decide the winner. Your Game: You will flip 3 three coins per turn and count how may times ALL three of your coins come up tails. You take 12 turns. Spouse's Game: Your spouse rolls 2 dice and counts how many times they rolls a sum of 6. your spouse takes 12 turns. Whoever has the highest total wins, picks the tv show while the other washes the dishes. a) What is the theoretical probability of your three coins all coming up tails? Please give your answer as the exact decimal. Do not round. P(TTT) = b) What is the theoretical probability of your spouse rolling a 6 with their two dice? Please give your answer as a decimal. Round to the fourth decimal point. P(6) = 20 points QUESTION 2 Let’s simulate this game: Flip 3 coins or use https://www.random.org/coins/?num=3&cur=60-usd.0001c to simulate your game. Record each event of your game below. Your spouse’s outcomes are already recorded. For your game, write your results as THT or TTT or HTH or THH or HTT, etc... T for tails and H for heads. Turn # Your 3 Coins Spouse's 2 Dice 1 1, 4 2 6, 6 3 4, 3 4 3, 3 5 2, 5 6 6, 5 7 2, 4 8 3, 1 9 2, 2 10 1, 5 11 4, 4 12 5, 3 a) How many times did you flip three tails? b) How many times did your spouse roll a sum of 6? c) Who won the game? You, your spouse or you tied? 15 points QUESTION 3 What is the relative frequency probability of you getting 3 tails with your coins for 12 turns? Relative Probability for you = / 10 points QUESTION 4 What is the relative frequency probability of your spouse getting a sum of 6 on two dice for 12 turns? Relative Probability for your spouse = /12 10 points QUESTION 5 If the number of turns were increased to 1,000, do you or your spouse have a better chance of winning? Explain why. My partner's game has the advantage since they have 5 ways out of 36 to win and I only have one way out of 8. My game has the advantage since the relative frequency probability should converge to the theoretical probability by the Law of Large Numbers and 1/8 > 5/36. My partner's game has the advantage since the relative frequency probability should converge to the theoretical probability by the Law of Large Numbers and 5/36 > 1/8 . My game has the advantage since I have three coins and my partner only has 2 dice. 10 points QUESTION 6 Since the probability of getting three tails and the probability of getting a sum of 6 on 2 coins are not exactly equal, this game is not fair. Find a way to change the rules or the number of turns to make it fair in which you still throws 3 coins and the spouse still rolls 2 dice. Describe your rule change and explain how your change would promote a fair contest. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Paragraph Arial 10pt P 0 WORDS POWERED BY TINY 10 points QUESTION 7 Use the following chart for the remaining problems in this quiz. A new scented candle (Hypno-Candle) is being tested which hypnotizes your spouse into watching whatever you want. There is a total of 1600 individuals in this study. Some are male, and some are female. Some were exposed to this hypnotizing candle, and some received the placebo candle scent. Here are the results after exposure. Is hypnotized Is not hypnotized Hypno-Candle scent Group 530 300 Placebo-Candle scent Group 50 720 Looking at all people in the study that were in the Hypno-Candle scent group, what is the probability that they become hypnotized? (Give your answer as a decimal and round to two decimal places) 5 points QUESTION 8 Using the chart above, What is the probability that a random person chosen from this study is hypnotized given that they were exposed to the Placebo-Candle scent? (Give your answer as a decimal and round to two decimal places) 5 points QUESTION 9 What is the probability that a random person chosen from this study was exposed to the Placebo-Candle scent given that they are hypnotized? (Give your answer as a decimal and round to two decimal places) 5 points QUESTION 10 Are the previous two questions asking the same thing? Explain why or why not for full credit. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Paragraph Arial 10pt P 0 WORDS POWERED BY TINY 10 points QUESTION 11 ACADEMIC INTEGRITY To make sure we are all on the same page, please read the University’s statement on academic integrity. I am certain you are capable of meeting my expectations for this course and am here to help you do so. If you are concerned about how well you are doing in the course, please come speak with me instead of considering academic misconduct. Academic Honesty Statement "I affirm that I am the student named above and that all the work on this test that I will submit is my work and my work alone. I also pledge to not discuss my answers or any of the problems with my classmates until everyone has finished the test." Agree Disagree 0 points QUESTION 12

This Quiz Is Over The Following Topics: Probability (Ch 7) Conditional Probability (Ch7) Law Of Large Numbers (Ch7)

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This Quiz Is Over The Following Topics: Probability (Ch 7) Conditional Probability (Ch7) Law Of Large Numbers (Ch7)

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