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Question.5643 - Greenfield High School emphasizes experiential and hands-on approaches to learning probability concepts. During a dedicated probability class, students actively engage in a variety of thoughtfully designed activities that encourage participation and practical understanding. By involving students in real-world applications and interactive tasks, the school ensures that learners grasp key principles of probability in an engaging and effective manner. Following are the four activities in which students will take part. Activity 1: In this activity, the class is split into two groups, each tasked with analyzing a specific event. Group A examines, where outcomes from rolling a standard six-sided die are categorized as either even (2, 4, 6) or odd (1, 3, 5). Meanwhile, Group B explores, which involves flipping a coin, resulting in "Heads" or "Tails," followed by rolling a six-sided die with outcomes ranging from 1 to 6. Question 1 Based on the described context above, define the following terms: Experiment Sample Space Event Outcome Probability Mutually exclusive events Independent events Activity 2 This activity conducted a survey involving 150 students to understand their participation in two workshops: Leadership (L) and Team Building (T). The survey results are organized and presented in the table provided below, summarizing how many students participated in each workshop, as well as any overlaps or exclusive participation for each activity. The results are summarized in the table below: Workshops Leadership (L) No Leadership (L')Total Team Building (T) 50 30 80 No Team Building (T') 20 50 70 Total 70 80 150 Question 2 Based on the described context above, Create a Venn Diagram to represent relationships between participation in Leadership and Team Building. b. Draw a tree diagram and show all the participation probabilities clearly. Activity 3 Students are given a box that contains 8 green balls and 4 yellow balls to solve two probability-based problems. In the first case, CASE 1, they are asked to draw a green ball followed by a yellow ball when the balls are replaced after each draw. In the second case, CASE 2, they need to draw a green ball followed by a yellow ball, but without replacing the balls between the draws. Question 3 Based on the described context above, Calculate the probability of CASE 1. Calculate the probability of CASE 2.

Answer Below:

Activity xxxxxxxx Experiment x process xxxxx produces xxxxxxx such xx rolling x die xx flipping x coin xxxxxx Space xxx set xx all xxxxxxxx outcomes xx an xxxxxxxxxx Event xxx subset xx the xxxxxx space xxxxxxx A xxxxxx result xx the xxxxxxxxxx Probability x number xxxxxxx and xxxx measures xxx likely xx event xx Mutually xxxxxxxxx Events xxxxxx that xxxxxx happen xx the xxxx time xxxxxxxxxxx Events xxxxxx where xxx outcome xx one xxxx not xxxxxx the xxxxxxx of xxx other xxxxxxxx Venn xxxxxxxxxxx diagram xxxxxxxx There xxx totally xxxxx with xxxxx balls x and xxxxxx balls x The xxxxxxxxxxx of xxxxxxx the xxxxx green xxxx is x G xx we xxxxxxx the xxxx there xxx still xxxxx The xxxxxxxxxxx of xxxxxxx the xxxxxx ball xx P x P x then x The xxxxxxxxxxx of xxxxxxx the xxxxx green xxxx is x G xxxxx removing xxx green xxxx there xxx balls xx the xxxxxxxxxxx of xxxxxxx one xxxxxx ball xx P x then x ReferencesIllowsky x Dean x Birmajer x Blount x Boyd x Einsohn x Helmreich x Kenyon x Lee x amp xxxx J xxxxxxxxxxxx statistics x Openstax xxxxx openstax xxx details xxxxx introductory-statistics- x Licensed xxxxx a xxxxxxxx Commons xxxxxxxxxxx

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