Given a deck of 52 playing cards, we place all cards in random order face up next to each other.Then we put a chip on each card that has at least one neighbour with the same face value (e.g., onthat has another queen next to it), we put a chip. Finally, we collect all chips that wereeachqueenplaced on the cards.For example, for the sequence of cardsA♡, 54, A4, 10O, 10♡, 104, 94, 30, 3♡, Q4, 34we receive 5 chips: One chip gets placed on each of the cards 100, 10♡, 104, 30, 3♡.(a) Let p5 be the probability that we receive a chip for the 5th card (i.e., the face value of the 5thcard matches the face value of one of its two neighbours). Determine p5 (rounded to 2 decimalplaces).(b) Determine the expected number of chips we receive in total (rounded to 2 decimal places).(c) For the purpose of this question, you can assume that the expectation of part (b) is 6 or smaller.Assume that each chip is worth v dollars. Further, assume that as a result of this game we receiveat least 24 dollars with probability 1/2 or larger. Prove that v > 2.

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Answered: Given a deck of 52 playing cards, we…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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In chess, a walk for a particular piece is a sequence of legal moves for that piece, starting from a square of your choice, that visits every square of the board. A tour is a walk that visits every square only once. (See Figure 5.13.) 5.13 Prove by induction that there exists a knight’s walk of an n-by-n chessboard for any n ≥ 4. (It turns out that knight’s tours exist for all even n ≥ 6, but you don’t need to prove this fact.)
Consider a tournament between N teams, each team playing each of the other teams. Show (by example) there is a tournament that might occur, where every team is beaten by some team.
There are N people numbered from 1 to N around a round table. Everyone has a different number in their hands between 1 and N. We start with the first person and count the number in his hand and ask the related person to leave the table. If the number in the card odd, we count clockwise. if it is even, we count counterclockwise. Ensure that all people leave the table. The first person to leave the table is the first person. In the sample scenario, the first integer value in the table_in.txt file indicates the number of people around the table, it is 5. The value of the card in the first person’s hand is written on the next line, it is 3. The value of the second person’s card is written on the next line, it is 1. In the table_out.txt file, print the order of people leaving the table. Sample scenario: table_in.txt 5 3 1 2 2 1 table_out.txt 1 4 2 3 5 Constraints N < 1,000,000 Do the solution in C/C++ with the Doubly Circular Linked List. Your codes should also be able to…
We have a list that stores the repeated heart-rate measurements for the same patient over several tests. Each inner-list is a test and for that test, the heart rate is monitored for some time while taking a few measurements. Next, we would like to calculate the average of the measurements for each test.heart_rate = [ [ 72, 75, 71, 73], # resting[ 91, 90, 94, 93], # walking slowly[ 130, 135, 139, 142], # running on treadmill[ 120, 118, 110, 105, 100, 98]] # after minute recoveryIn your code, define a function calculate_average_heart_rates() that accepts the list heart_rate as its only input argument. Inside the function, use nested loops to calculate the average heart rate during each test scenario. This function should return a list that contains the average heart rate values of a patient for the four test scenarios.Write unit tests
Start with a pile of n stones and successively split a pile into two smaller piles until each pile has only one Each time a split happens, multiply the number of stones in each of the two smaller piles. (For example, if a pile has 15 stones and you split it into a pile of 7 and another pile of 8 stones, multiply 7 and 8.) The goal of this problem is to show that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2. Using strong mathematical induction, prove that no matter how the pile of n stones are split, the sum of the products computed at each split is equal to n(n - 1)/2.
A drawer contains 7 pair of socks where 8 socks are white, and 6 are red. In how many ways we can take 14 random socks out of the drawer so each sock is next to its matching pair. a. 441 ways b. 42 ways c. 1225 ways d. 70 ways
Suppose that the only currency were 3-dollar bills and 10-dollar bills. Show that every amount greater than 17 dollars could be made from a combination of these bills.
In a tournament, there are n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of [n(n-1)/2] matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all [n(n-1)/2] matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English. PLease give the total time complexity.
In a tournament, there are n participating teams are labelled from 1 to n. Each pair of teams will play against each other exactly once. Thus, a total of [n(n-1)/2] matches will be held, and each team will compete in n − 1 of these matches. There are only two possible outcomes of a match: 1. The match ends in a draw, in which case both teams will get 1 point. 2. One team wins the match, in which case the winning team gets 3 points and the losing team gets 0 points. Design an algorithm which runs in O(n2 ) time and provides a list of results in all [n(n-1)/2] matches which: (a) ensures that all n teams finish with the same points total, and (b) includes the fewest drawn matches among all lists satisfying (a). Do not write the code, give steps and methods. Explain the steps of algorithm, and the logic behind these steps in plain English
X-Kingdom has trapped n number of soldiers of their opponent. They want to execute them. They created a strategy so that the prisoners will kill each other and at the end one prisoner will be alive and eventually released. As part of the process, they assigned each trapped soldier a sequence number starting from 1 and ending at n. If n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1 is killed. Finally, the person at position 5 is killed. So, the person at position 3 survives. If n = 7 and k = 3, then the safe position is 4. The people at positions 3, 6, 2, 7, 5, 1 are killed in order, and the person at position 4 survives. Input:n and k Output:Print the list of prisoners in reverse order from n to 1Then reverse the list to print it in correct order from 1 to nDisplay the position number who will survive. You must have to use circular doubly linked list for your solution.
X-Kingdom has trapped n number of soldiers of their opponent. They want to execute them. They created a strategy so that the prisoners will kill each other and at the end one prisoner will be alive and eventually released. As part of the process, they assigned each trapped soldier a sequence number starting from 1 and ending at n. If n = 5 and k = 2, then the safe position is 3. Firstly, the person at position 2 is killed, then person at position 4 is killed, then person at position 1 is killed. Finally, the person at position 5 is killed. So, the person at position 3 survives. If n = 7 and k = 3, then the safe position is 4. The people at positions 3, 6, 2, 7, 5, 1 are killed in order, and the person at position 4 survives. Input:n and k Output:Print the list of prisoners in reverse order from n to 1Then reverse the list to print it in correct order from 1 to nDisplay the position number who will survive. You must have to use circular doubly linked list for your solution. You…
Mastermind is a code-breaking game for two players. In the original real-world game, one player A selects 4 pegs out of 6 colors and puts them in a certain fixed order; multiples of colors are possible (for example, red-green red-green). His opponent B does not know the colors or order but has to find out the secret code. To do so, B makes a series of guesses, each evaluated by the first player. A guess consists of an ordered set of colors which B believes is the code. The first player A evaluates the guess and feeds back to B how many positions and colors are correct. A position is correct ("black") if the guess and the secret code have the same color. Additional colors are correct ("white"), if they are in the guess and the code, but not at the same location. For example1 2 3 4secret: red-green red greenguess: red blue green purpleresults in one correct position ("black = 1") for the red peg at position one and one additional correct color ("white=1") for the green peg in the guess.…

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