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Tracie spins the four-colored spinner shown below. She records the total number of times the spinner lands on the color red and constructs a graph to visualize her results. Which of the following statements is TRUE?  If Tracie spins the spinner 1,000 times, it would land on red close to 250 times.  If Tracie spins the spinner 1,000 times, the relative frequency of it landing on red will remain constant.  If Tracie spins the spinner 4 times, it will land on red at least once.  The theoretical probability of the spinner landing on red will change with every spin completed. RATIONALE If we make the assumption that the area of the colors represents the true proportion, then each color is equally weighted. Since there are four colors we would expect them to come up roughly 1/4 of the time. So on 1000 rolls the expected value = n*p = 1000*0.25 = 250. CONCEPT Law of Large Numbers/Law of Averages 2 Two sets A and B are shown in the Venn diagram below. Which statement is TRUE?  There are a total of 17 elements shown in the Venn diagram.  Set A has 12 elements.  Set B has 5 elements.  Sets A and B have 15 common elements. RATIONALE The number of elements of Set A is everything in Circle A, or 10+2 = 12 elements. The number of elements of Set B is everything in Circle B, or 5+2 = 7 elements, not 5 elements. The intersection, or middle section, would show the common elements, which is 2 elements, not 15 elements. To get the total number of items in the Venn diagram, we add up what is in A and B and outside, which is 10+2+5+3 = 20 elements, not 17 elements. CONCEPT Venn Diagrams 3 Using the Venn Diagram below, what is the conditional probability of event B occurring, assuming event A has happened [P(B|A)]?  0.41  0.63  0.24  0.77 RATIONALE To get the probability of B given A has occurred, we can use the following conditional formula: The probability of A and B is the intersection, or overlap, of the Venn diagram, which is 0.41. The probability of A is all of Circle A, or 0.24 + 0.41 = 0.65. CONCEPT Conditional Probability 4 The gender and age of Acme Painting Company's employees are shown below. Age Gender 23 Female 23 Male 24 Female 26 Female 27 Male 28 Male 30 Male 31 Female 33 Male 33 Female 33 Female 34 Male 36 Male 37 Male 38 Female 40 Female 42 Male 44 Female If the CEO is selecting one employee at random, what is the chance he will select a male OR some

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MATH 1280 Milestone 3_Introduction to Statistics (2020) – University of the People Tracie spins the four-colored spinner shown below. She records the total number of times the spinner lands on the col...

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