Section 4 Lab (1)

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Clemson University *

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3090

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Statistics

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Apr 3, 2024

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STAT 3090 S ECTION 4 L AB S PRING 2024 P ROBABILITY N AME : Megan McCauley O BJECTIVES : Upon successful completion of this assignment, you will be able to…  Write a sample space for a probability experiment  Assign probabilities to events  Use the compliment rule, addition rule and multiplication rule,  Determine if two events are mutually exclusive  Determine if two events are independent or dependent  Apply probability rules to solve a complex problem If you would like to type formulas and your calculations into Word, you may find this YouTube video on using the Microsoft Equation Editor helpful. https://www.youtube.com/watch?v=GdF5kYIoh-U Part One 1. Spin the Pointer (21 points) To show their appreciation, Delectable Delights decided to put on a carnival for its employees. One of the games at the carnival was Spin the Pointer, which uses a spinner like the one pictured here. A carnival ticket is required to play the game. The spinner is divided into 8 equally sized sectors. Thus, the spinner has an equal probability of landing in each sector. 1

STAT 3090 S ECTION 4 L AB S PRING 2024 P ROBABILITY (a) What is the sample space for the spinner game? Use appropriate symbol . (3 points) S = {1, 2, 3, 4, 5, 6, 7, 8} (b) What is the probability of landing in each sector? Use probability notation . (3 points) 0 ≤ 1/6 ≤ 1 (c) The number shows on each sector is the money a player receives after playing one spin of the game. That is, if the spinner lands in Sector 1 or Sector 5, the player receives $1.00; if the spinner lands in Sector 3, the player receives $5.00; if the spinner lands in the rest sectors, the player receives nothing. i. Let event A be the player receives $1.00 after one spin of the game. What is the probability of event A occurring? Use probability notation . (3 points) P(A) = 0 ≤ 1/3 ≤ 1 ii. Let event C be the player receives $5.00 after one spin of the game. What is the probability of event C occurring? Use probability notation . (3 points) P(C) = 0 ≤ 1/6 ≤ 1 2

STAT 3090 S ECTION 4 L AB S PRING 2024 P ROBABILITY iii. Let event D be the player receives $0.00 after one spin of the game. What is the probability of event D occurring? Use probability notation . (3 points) P(D) = 0 ≤ ½ ≤ 1 iv. Describe the complement of event D. Calculate the probability of the complement of event D using the complement rule. Use probability notation . (3 points) The complement of event D is winning any amount of money in the spinner game. P(D c ) = 1 – P(D) P(D c ) = 1- ½ P(D c ) = 0 ≤ ½ ≤ 1 (d) Suppose a player needs to pay for the carnival ticket costs $1.00 before playing every spin of the game. What is the probability the player has a profit of $4.00 after one spin of the game? Explain how you obtained your answer. (3 points) P(C) = 0 ≤ 1/6 ≤ 1 because for the player to have a profit of $4 after doing the spinning game one time and spending $1 on a ticket, event C would have to happen. 3

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STAT 3090 S ECTION 4 L AB S PRING 2024 P ROBABILITY Part Two 2. Star Wars Promotion (39 points) Delectable Delights is very excited to announce that they will provide advertising support for the Star Wars Episode IX movie. They will feature 5 of the Resistance characters as toy prizes in their cereals Cosmic Crisps , Intergalactic Granola, and Resistance Rice Flakes . A shipment of 1000 cereal boxes has been prepared for distribution. The file Star Wars Promotion.jmp contains the data about the cereal names and which toys are included in the boxes. ** You need to download the Star Wars Promotion.jmp from Canvas and then use JMP to open it.** **If you use CUAPPS , please make sure to download file from Canvas and then upload your Star Wars Promotion.jmp file from your local laptop drive to Remote PC folder or OneDrive-Clemson University , CUAPPS cannot open file from local drive of your own laptop** (a) Using the Tabulate function in JMP, create a table showing the 3 cereals and the 5 types of characters that are in the boxes. Step 1: Open the file Star Wars Promotion.jmp by JMP, go to Analyze >> Tabulate . Step 2: Drag Cereal to “ Drop zone for columns ”. Drag Character to the first column of the table formed by Cereal. 4

STAT 3090 S ECTION 4 L AB S PRING 2024 P ROBABILITY Step 3: Select “Add Aggregate Statistics” . Step 4: Copy and paste your table below. You can use screenshot. (4 points) (b) Suppose you randomly select one box of cereal from this shipment. What is the probability that the prize is the character C-3PO? Use probability notation . You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) P(C-3PO) = 0 ≤ 245/1000 ≤ 1 5

STAT 3090 S ECTION 4 L AB S PRING 2024 P ROBABILITY (c) Suppose you randomly select one box of cereal from this shipment. What is the probability it is not Cosmic Crisps ? Use probability notation . You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) P(CC c ) = 0 ≤ 700/1000 ≤ 1 (d) In case you do not follow the Star Wars Movies, Rey and Finn are humans, Chewbacca is a Wookie, and BB8 and C3PO are droids (robots). What is the probability of selecting a random box of cereal that is Intergalactic Granola and contains a droid? Use probability notation . You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) Event A: Intergalactic Granola. Event B: droid. P(A and B) = 0 ≤ 285/1000 ≤ 1 (e) What is the probability of selecting a random box of cereal that is Intergalactic Granola or contains a droid? Use probability notation . You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) Event A: Intergalactic Granola. Event B: droid. P(A or B) = P(A) + P(B) - P(A intersects B) P(A) = 400/1000 P(B) = 490/1000 P(A or B) = 400/1000 + 490/10000 – 285/1000 P(A or B) = 0 ≤ 605/1000 ≤ 1 (f) Given the event that you selected a box of Intergalactic Granola from the shipment, what is the probability that your prize is the character C-3PO? Use probability notation . You may write your final answer as a fraction (no need to reduce it) or decimal. (4 points) P(C-3PO) = 0 ≤ 180 ≤ 400 (g) Suppose that your favorite character is Chewbacca the Wookie. Which cereal type should you select in order to have the highest probability of obtaining a Chewbacca toy? 6

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STAT 3090 S ECTION 4 L AB S PRING 2024 P ROBABILITY Justify your answer using probabilities numerically . An intuitive description without using probabilities won’t receive any credit. Using probabilities without showing their numerical values won’t receive full credit. (5 points) I should choose Resistance Rice Flakes because it has the highest probability (80/200) of having Chewbacca as compared to Intergalactic Granola (55/200) and Cosmic Crisps (65/200). (h) Are the events selecting a box of Intergalactic Granola and getting the character C-3PO as the prize independent? Justify your answer using probabilities numerically . An intuitive description without using probabilities won’t receive any credit. Using probabilities without showing their numerical values won’t receive full credit. (Hint: Use a test for independence.) (5 points) 180/1000 = (400/1000)*(245/1000) 0.18 ≠ 0.098, not equal so not independent (i) Select two events from this table that you believe are mutually exclusive. Justify your answer using probabilities numerically . An intuitive description without using probabilities won’t receive any credit. Using probabilities without showing their numerical values won’t receive full credit. (5 points) 3. Complete WebAssign Section 4 . (40 points) 7

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