Group Names: A recent study conducted in the U.S. found that approximately 65% of adults drink coffee daily and 52% drink tea daily. 21% of adults in the U.S. drink both coffee and tea on a daily basis. Drag the textboxes to create an appropriate Venn diagram and answer the following probability questions. Coffee Tea 0.65 0.04 0.21 0.40 0.32 0.44 0.96 0.31 0.52 Find the probability that a randomly chosen adult drinks coffee or tea. Find the probability that a randomly chosen adult drinks neither coffee or tea. Find the probability that a randomly chosen adult drinks tea given they drink coffee.Written Homework Assignment Supplemental Topic: Venn Diagrams and Probability Trees MATH-133 Online Statistics Directions: Write out your solutions to the questions below on a separate sheet of paper. Then scan your written work, save it as a PDF file, and submit it on Canvas. Assignment: (22 pain ts total) 1) Suppose the probability that a US resident has traveled to Canada is 0.12, to Mexico is 0.20, and to both countries is 0.04. Round your answers to two decimal places. (11 pts) 3) Create a Venn diagram for the scenario above. In) What is the probability that a US resident chosen at random has traveled to Canada but not Mexico? c) What is the probability that a US resident chosen at random has traveled to either Canada or Mexico? d) What is the probability that a US resident chosen at random has not traveled to either Canada or Mexico? e) What is the probability that a US resident chosen at random has traveled to Mexico given they have traveled to Canada? 2) Historically, two rival teams have been closely matched, and during a regular season, they play each other twice. The probability that Team A wins the first game is 0.45. If Team A wins the first game, the probability that they also win the second game is 0.30. If they lose the first game, the probability that Team A wins the second game is 0.65. For ports {or-d), do not round your answers. For part (e) round your answer to three decimal places. {11 pts) 3) Create a tree diagram for the scenario above. b) What is the probability that Team A wins both games? c) What is the probability that Team A wins exactly one game? d) What is the probability that Team A wins the second game? e) Given Team A wins the second, what is the probability they won the first game? Written Homework Assignment Supplemental Topic: Contingency Tables MATH-133 Online Statistics Directions: Write out your solutions to the questions below on a separate sheet of paper. Then scan your written work, save it as a PDF file, and submit it on Canvas. Late assignments will receive a grade of zero unless prior arrangements are made with me. Assignment: (21 points total) 1) A group of 200 students classified themselves in terms of personality (introvert or extrovert) and color choice (red, yellow, green or blue) with the purpose of seeing whether there is a relationship between personality and color preference. The following table summarizes the findings. Color Preference Personality Introvert 10 Type Extrover'l: 90 a} What is the probability that a randomly chosen student in this study classified themselves as extroverted? Give both the fraction and the decimal final answer. b} Given a student chose yellow as their favorite color, what is the probability that they classified themselves as extroverts? Give both the fraction and the decimal final answer. c} Given a student chose red as their favorite color, what is the probability that they classied themselves as extroverts? Give both the fraction and the decimal final answer. d} Give the marginal distribution of Personality Type. Give the fractions and percents. e) Give the conditional distribution of Personality Type for those that chose blue as their favorite color. Give the fractions and percents. 2) Consider the following bar graphs below. The first shows the marginal distribution for Personality Type and the second shows the conditional distribution of Personality Type for each Color Preference group. Two variables are independent if the distribution of one variable is the same when looking at the data as a whole in comparison to the distribution of that same variable across each group of the second variable. Essentially, if the distribution doesn't change, then the second variable has no influence on the first and we can say that they variables are independent. On the other hand, if the distribution does change, then the variables are not independent and there is an association between the two. For example, we can see in the graphs below that the distribution for Personality Type (75% extroverts, 25% introverts) is not the same for each Color Preference group. In particular, someone who chose red as their preferred color is more likely to describe themselves as extroverted. Thus, we can see from these graphs that Personality Type and Color Preference are not independent. Mm: [Mlh I'm} When we study probabilities, we can simplify this process by looking at conditional probabilities instead of the entire conditional distribution. Because of the properties of probabilities, we can conclude that if we see a change in any single event, then we can conclude that the variables themselves are not independent. For example, we can compare the P(extrovert) = 0.75 with P(extrovert | red) = 0.9 and we can see that the event of being an extrovert changes when looking at the blue group. For this problem: a) Compare P(introvert) with P(introvert | blue) and make a conclusion about whether the variables are independent or not. Be sure to use the table at the beginning of this assignment to get your numbers and use the graphs to check your work. b) Compare P(red) with P(red | introvert). Can you make the same conclusion on independence as you did in part (a)