Q2 The Powerball Lottery 15 Points The Powerball lottery is based on a random drawing of six balls from two machines. One machine contains 69 white balls (labeled 1 through 69) and the other machine contains 26 red balls (labeled 1 through 26). To determine the winning numbers, the gamemaster draws five white balls from the first machine and one red ball (the "Powerball") from the second machine (assume all outcomes are equally likely). A player in the Powerball lottery picks five different numbers between 1 and 69 (inclusive) and a sixth number between 1 and 26 (inclusive), which may duplicate one of the first five numbers. For each of the following questions, 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. Q2.2 What is the probability that a player wins $100 by matching exactly four of the first five numbers (in any order), but not the sixth number?
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- A Marble Game is played with M marbles on a square board. The board is divided into NxN squares, andM of those squares contain holes. Marbles and holes are numbered from 1 to M. The goal of the Marblegame is to roll each marble into the hole that has the same number. A game board may contain walls.Each wall is one unit long and stands between two adjacent unit squares. Two squares are consideredadjacent if and only if they share a side.At the beginning of the game, all marbles are placed on the board, each in a different square. A “move”consists of slightly lifting a side of the game board. Then all marbles on the board roll downward towardthe opposite side, each one rolling until it meets a wall or drops into an empty hole, or until the nextsquare is already occupied by another marble. Marbles roll subject to the following restrictions: Marbles cannot jump over walls, other marbles, or empty holes Marbles cannot leave the board (The edge is a wall) A unit square can contain at most…The game of Chomp is played by two players. In this game, cookies are laid out on a rectangular grid. The cookie in the top-left position is poisoned. The two players take turns making moves; at each move, a player is required to eat a remaining cookie, together with all cookies to the right and/or below (that is all the remaining cookies in the rectangle, in which the first cookie eaten is the top left corner). The loser is the player who has no choice but to eat the poisoned cookie. Prove that if the board is square (and bigger than 1 × 1) then the first player has a winning strategy.A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, theprincipal plays the following game: She asks the first student to open all the lockers. She then asks the secondstudent to close all the even-numbered lockers. The third student is asked to check every third locker. If it isopen, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourthlocker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continuethis game. In general, the nth student checks every nth locker. If it is open, the student closes it; if it is closed,the student opens it. After all the students have taken turns, some of the lockers are open and some are closed.The program below, when ran, will prompt the user to enter the number of lockers in the school. After thegame is over, the program will output the number of lockers and the lockers numbers of the lockers…
- You will be given a square chess board with one queen and a number of obstacles placed on it. Determine how many squares the queen can attack. A queen is standing on an chessboard. The chess board's rows are numbered from to , going from bottom to top. Its columns are numbered from to , going from left to right. Each square is referenced by a tuple, , describing the row, , and column, , where the square is located. The queen is standing at position . In a single move, she can attack any square in any of the eight directions (left, right, up, down, and the four diagonals). In the diagram below, the green circles denote all the cells the queen can attack from : There are obstacles on the chessboard, each preventing the queen from attacking any square beyond it on that path. For example, an obstacle at location in the diagram above prevents the queen from attacking cells , , and : Given the queen's position and the locations of all the obstacles, find and print the number of…You have a fence post located at the point (x,y) where a goat is tethered by a rope. You also have a house, which is a rectangle with diagonally opposite corners at the points bottom-left: (x1,y1) and top-right: (x2,y2). You want to pick a length of rope that guarantees the goat cannot reach the house. Determine the minimum distance from the fence post to the house, so that you can make sure to use a shorter rope. Recall that the distance formula is: sqrt( (x2−x1)^2+(y2−y1)^2 ) The input consists of a single line containing six space-separated integer values: x, y, x1, y1, x2, and y2. You are guaranteed that x1<x2 and y1<y2, and that (x,y) is strictly outside the axis-aligned rectangle with corners at (x1,y1) and (x2,y2). Return the minimum distance from the goat’s post to the house as a floating-point value from main(). Learning Objectives Be able to create a program with a lesser template. Be able to calculate the min/max of integers. Be able to write a mathematical…Correct answer will upvoted else downvoted Petya found out with regards to another game "Kill the Dragon". As the name recommends, the player should battle with mythical beasts. To overcome a mythical serpent, you need to kill it and shield your palace. To do this, the player has a crew of n legends, the strength of the I-th saint is equivalent to man-made intelligence. As per the principles of the game, precisely one saint should go kill the mythical serpent, all the others will shield the palace. On the off chance that the mythical serpent's protection is equivalent to x, you need to send a saint with a strength of essentially x to kill it. Assuming the winged serpent's assault power is y, the absolute strength of the saints protecting the palace ought to be ssentially y. The player can build the strength of any legend by 1 for one gold coin. This activity should be possible quite a few times. There are m winged serpents in the game, the I-th of them has protection equivalent to…
- the starting position of a simple game. Player A moves first. The two players take turns moving, and each player must move his token to an open adjacent space in either direction. if the opponent accupies an adjacent space, then a player may jump over the opponent to the next open space if any. (for example, if a is on 3 and b is on 2, then a may move back to 1.) the game ends when one player reaches the opposite end of the board. If player a reaches space 4 first, then the value of the game to a is +1; if player b reaches space 1 first, then the value of the game to a is -1 consider the two player game described in figure 5.17. a. draw the complete game tree, using the following conventions: 1. write each state as (sa,sb), where sa and sb denote token locations. 2. put each terminal state in a square box and write its game value in a circle. 3. put loop states (states that already appear on the path to the root) in double square boxes. since their value is unclear, annotate each with…Bomberman lives in a rectangular grid. Each cell in the grid either contains a bomb or nothing at all. Each bomb can be planted in any cell of the grid but once planted, it will detonate after exactly 3 seconds. Once a bomb detonates, it's destroyed — along with anything in its four neighboring cells. This means that if a bomb detonates in cell , any valid cells and are cleared. If there is a bomb in a neighboring cell, the neighboring bomb is destroyed without detonating, so there's no chain reaction. Bomberman is immune to bombs, so he can move freely throughout the grid. Here's what he does: Initially, Bomberman arbitrarily plants bombs in some of the cells, the initial state. After one second, Bomberman does nothing. After one more second, Bomberman plants bombs in all cells without bombs, thus filling the whole grid with bombs. No bombs detonate at this point. After one more second, any bombs planted exactly three seconds ago will detonate. Here, Bomberman stands back and…Bomberman lives in a rectangular grid. Each cell in the grid either contains a bomb or nothing at all. Each bomb can be planted in any cell of the grid but once planted, it will detonate after exactly 3 seconds. Once a bomb detonates, it's destroyed — along with anything in its four neighboring cells. This means that if a bomb detonates in cell , any valid cells and are cleared. If there is a bomb in a neighboring cell, the neighboring bomb is destroyed without detonating, so there's no chain reaction. Bomberman is immune to bombs, so he can move freely throughout the grid. Here's what he does: Initially, Bomberman arbitrarily plants bombs in some of the cells, the initial state. After one second, Bomberman does nothing. After one more second, Bomberman plants bombs in all cells without bombs, thus filling the whole grid with bombs. No bombs detonate at this point. After one more second, any bombs planted exactly three seconds ago will detonate. Here, Bomberman stands back and…
- In the Dice Roll game, the player begins with a score of 1000. The player is prompted for the numberof points to risk and a second prompt asks the player to choose either high or low. The player rollstwo dice and the outcome is compared to the player’s choice of high or low. If the dice total is between2 and 6 inclusive, then it is considered “low”. A total between 8 and 12 inclusive is “high”. A total of7 is neither high nor low, and the player loses the points at risk. If the player had called correctly, thepoints at risk are doubled and added to the total points. For a wrong call, the player loses the points atrisk. Create a DiceRollGame application that uses a DRPlayer object based on this specification. TheDRPlayer object should have two Die member variables that represent the dice. The Die class shoulduse a random number generator to determine the outcome in a roll() method. Application outputshould look similar to:In the card game War, a deck of playing cards is divided between two players. Each player exposeda card; the player whose card has the higher value wins possession of both exposed cards. Createa console-based computerized game of War named WardCardGame in which a standard 52-carddeck is randomly divided between two players, one of which is the computer. Reveal one card forthe computer and one card for the player at a time. Award two points for the player whose cardhas the higher value. (For this game, the king is the highest card, followed y the queen and jack,then the numbers 10 down to 2, and finally the ace.) if the computer and player expose cards withequal values in the same turn, award one point to each. At the end of game, all 52 cards shouldhave been played only once, and the sum of the player’s and computer’s score will be 52.Use an array of 52 integers to store unique values for each- card. Write a method name FillDeck()that places 52 unique values into this array. Write…In the card game War, a deck of playing cards is divided between two players. Each player exposeda card; the player whose card has the higher value wins possession of both exposed cards. Createa console-based computerized game of War named WardCardGame in which a standard 52-carddeck is randomly divided between two players, one of which is the computer. Reveal one card forthe computer and one card for the player at a time. Award two points for the player whose cardhas the higher value. (For this game, the king is the highest card, followed y the queen and jack,then the numbers 10 down to 2, and finally the ace.) if the computer and player expose cards withequal values in the same turn, award one point to each. At the end of game, all 52 cards shouldhave been played only once, and the sum of the player’s and computer’s score will be 52.Use an array of 52 integers to store unique values for each- card. Write a method name FillDeck()that places 52 unique values into this array. Write…