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Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 3. A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), 4 possible suits (spades, clubs, hearts, diamonds), and 13 cards in each suit (one of each rank). A hand of 9 cards is drawn from a standard deck of 52 cards (assume all outcomes are equally likely). 3.1 What is the probability that a hand of 9 cards is all the same suit (for example, all hearts)? 3.2 What is the probability that a hand of 9 cards has four cards of one suit and five cards of another suit (for example, four hearts and five diamonds)? 3.3 What is the probability that a hand of 9 cards has three cards of one rank, three cards of a second rank, and three cards of a third rank (for example, three A's, three 4's, and three K's)?

Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 3. A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), 4 possible suits (spades, clubs, hearts, diamonds), and 13 cards in each suit (one of each rank). A hand of 9 cards is drawn from a standard deck of 52 cards (assume all outcomes are equally likely). 3.1 What is the probability that a hand of 9 cards is all the same suit (for example, all hearts)? 3.2 What is the probability that a hand of 9 cards has four cards of one suit and five cards of another suit (for example, four hearts and five diamonds)? 3.3 What is the probability that a hand of 9 cards has three cards of one rank, three cards of a second rank, and three cards of a third rank (for example, three A's, three 4's, and three K's)?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 3. A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), 4 possible suits (spades, clubs, hearts, diamonds), and 13 cards in each suit (one of each rank). A hand of 9 cards is drawn from a standard deck of 52 cards (assume all outcomes are equally likely). 3.1 What is the probability that a hand of 9 cards is all the same suit (for example, all hearts)? 3.2 What is the probability that a hand of 9 cards has four cards of one suit and five cards of another suit (for example, four hearts and five diamonds)? 3.3 What is the probability that a hand of 9 cards has three cards of one rank, three cards of a second rank, and three cards of a third rank (for example, three A's, three 4's, and three K's)?
Transcribed Image Text:Part I: Probability For each of the following problems, you should write your answer as an expression. Do not give the final numeric value. For example, you should write C(4,2)/24 instead of 0.375. 3. A standard deck of playing cards consists of 52 cards. Each card has a rank and a suit. There are 13 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K), 4 possible suits (spades, clubs, hearts, diamonds), and 13 cards in each suit (one of each rank). A hand of 9 cards is drawn from a standard deck of 52 cards (assume all outcomes are equally likely). 3.1 What is the probability that a hand of 9 cards is all the same suit (for example, all hearts)? 3.2 What is the probability that a hand of 9 cards has four cards of one suit and five cards of another suit (for example, four hearts and five diamonds)? 3.3 What is the probability that a hand of 9 cards has three cards of one rank, three cards of a second rank, and three cards of a third rank (for example, three A's, three 4's, and three K's)?
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