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Home Question Bank Math Probability Archive 2024 December 04

Probability Questions from Dec 04,2024

Browse the Probability Q&A Archive for Dec 04,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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4 Permutations and Probabilities: 20 pts, Part A: 10 pts. You are tasked with organizing a group of 6 people: Allice, Bob, Charlie, David, Eva, and Frank. How many different ways can you arrange these 6 people in a line? Show your work to receive full credit. Part B: 10 pts. If the arrangement from Part A must have Alice and Bob standing next to each other, what is the probability that Alice and Bob will be next to each other in a random arrangement? Show your work to receive full credit. 3. Combinations and Probabilities: 20 pts. You are tasked with creating a code using the following three conditions: 1. The code must consist of exactly 4 characters. 2. Each character can be one of the following: A, B, C, or D. 3. The code can repeat characters, but the first character must be different from the last character. How many different codes can you create based on these condi- tions? You MUST show all of your steps to receive full credit. After a particular surgery, patients are placed in an intensive care unit (ICU) until their condition stabilizes. Then they are transferred to a special care ward (SCW), where they remain until they are released from the hospital. In a particular metropolitan area, a study of hospital records produced the following data: each day \( 2 \% \) of the patients in the ICU died, \( 49 \% \) were transferred to the SCW, and the remainder stayed in the ICU. Furthermore, each day \( 3 \% \) of the patients in the SCW developed complications and were returned to the ICU, \( 1 \% \) died while in the SCW, \( 22 \% \) were released from the hospital, and the remainder stayed in the SCW. A) In the long run, what percentage of the patients in the ICU are released from the hospital? \( 91.43 \% \) (Round to two decimal places as needed.) B) In the long run, what percentage of the patients in the SCW die without ever being released from the hospital? \( \square \% \) (Round to two decimal places as needed.) After a particular surgery, patients are placed in an intensive care unit (ICU) until their condition stabilizes. Then they are transferred to a special care ward (SCW), where they remain until they are released from the hospital. In a particular metropolitan area, a study of hospital records produced the following data: each day \( 2 \% \) of the patients in the ICU died, \( 49 \% \) were transferred to the SCW, and the remainder stayed in the ICU. Furthermore, each day \( 3 \% \) of the patients in the SCW developed complications and were returned to the ICU, \( 1 \% \) died while in the SCW, \( 22 \% \) were released from the hospital, and the remainder stayed in the SCW. A) In the long run, what percentage of the patients in the ICU are released from the hospital? \( \square \% \) (Round to two decimal places as needed.) The Fundamental Counting Principle (FCP) store enlls three types of shirts: red, blue, and green. Each shirt is available three different sizes: small, medium, and large. a.) Draw a tree diagram that represents all the possible combinations of Use the tree diagram to calculate the total number of different shirt com- tions (color and size) available in the store (5 pts). Suppose a customer randomly selects one shirt from the store. What is robability that the selected shirt is cither blue or large in size? (5pts) What is the probability of a customer purchasing a shirt that is large irple? (5pts) Question 4 (1 point) In order for 2 events to be mutually exclusive, they occur at the same time. True False Question 3 (1 point) Flipping a coin once, then flipping it again is an example of: independent events dependent events Question 2 (1 point) Using the definition of probability, what are the chances of pulling a King out of a deck of 52 cards? \( 1 / 52 \) \( 4 / 52 \) \( 8 / 52 \) \( 2 / 52 \) Question 1 (1 point) Choose 3 ways a sample space can be represented. (you will select 3 of these) Select 3 correct answer(s) List Taragraph Tree Diagram Equation There are 10 people at a meeting and there are 3 different door prizes to give out. How many ways can we select 3 people to receive the door prizes?
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