Q2.1 A player wins the jackpot ($98 million) if the first five numbers picked match the numbers on the five white balls (in any order) and the sixth number picked matches the number on the red ball. What is the probability that a player wins the jackpot? 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.
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- Nim is a two-player game played with several piles of stones. You can use as many piles and as many stones in each pile as you want, but in order to better understand the game, we'll start off with just a few small piles of stones (see figure 1 below). Pile 1 Pile 1 Pile 2 The two players take turns removing stones from the game. On each turn, the player removing stones can only take stones from one pile, but they can remove as many stones from that pile as they want (please note, a player must remove atleast 1 stone from a pile during his/her turn). If they want, they can even remove the entire pile from the game! The winner is the player who removes the final stone (avoid taking the last stone - see figure 2 below). Pile 2 Pile 3 Pile 3 Let's say its Max (player 1) turn to play. Then Max can win by simply removing a stone from Pile 2 or Pile 3 Draw a game tree (upto depth level 2) for the given version of the Nim game. Please consider figure 1 as your initial game configuration/state…Tic-Tac-Toe For this question, you will be implementing a simple Tic-Tac-Toe game without the graphics. Here is how it works: • First, it is randomly determined if the user starts the game or the computer and this information is shown to the user. The player who starts always starts as "X". • The players (computer and the user) will then take turns in playing. The computer will choose a random empty spot on its turn. The user enters its choice in the console. • Each of the empty spots have a corresponding number that the players choose on their turn. If the user enters anything other than the number of an empty spot (not yet filled with "X" or "O"), it will not be accepted, and they will be prompted to enter a correct number. 2 4 7 8 • After each turn, two things need to be done: 1) displaying the updated board 2) checking if anyone has won (it should be printed who has won – the user or the computer). The game goes on until someone wins or until all the 9 empty spots are filled and no…Description: Raghu and Sayan both like to eat (a lot) but since they are also looking after their health, they can only eat a limited amount of calories per day. So when Kuldeep invites them to a party, both Raghu and Sayan decide to play a game. The game is simple, both Raghu and Sayan will eat the dishes served at the party till they are full, and the one who eats maximum number of distinct dishes is the winner. However, both of them can only eat a dishes if they can finish it completely i.e. if Raghu can eat only 50 kCal in a day and has already eaten dishes worth 40 kCal, then he can't eat a dish with calorie value greater than 10 kCal. Given that all the dishes served at the party are infinite in number, (Kuldeep doesn't want any of his friends to miss on any dish) represented by their calorie value(in kCal) and the amount of kCal Raghu and Sayan can eat in a day, your job is to find out who'll win, in case of a tie print "Tie" (quotes for clarity). Input: First line contains…
- Game Description: Pig is a game that has two players (in our case one human and one computer) that alternate turns. Each player’s goal is to get 100 points rolled on a normal six-sided die first. Each turn consists of the rolling the die repeatedly until you get a 1 or decide to stop. As long as you roll a 2-6, you will add this amount to your total for that turn. But if you roll a 1 during your turn, your turn ends and you receive zero points for that entire turn (erasing all of the progress you made since you last agreed to stop). If you decide to stop rolling at any point in your turn, your points for that turn are then added to the overall score. The overall score is then safe from future rolls. The trick is knowing how long to push it before we should stop and save our gains. See end of this document for an example of a game of pig we should write coding as below In order to explore what is the best strategy for the computer player (i.e. at what score do we stop each computer…Othello is played as follows: Each Othello piece is white on one side and black on the other. When a piece is surrounded by its opponents on both the left and right sides, or both the top and bottom, it is said to be captured and its color is flipped. On your turn, you must capture at least one of your opponent's pieces. The game ends when either user has no more valid moves. The win is assigned to the person with the most pieces. Implement the object-oriented design for Othello.You are hired by a game design company and one of their most popular games is The Journey. The game has a ton of quests, and for a player to win, the player must finish all the quests. There are a total of N quests in the game. Here is how the game works: the player can arbitrarily pick one of the N quests to start from. Once the player completes a quest, they unlock some other quests. The player can then choose one of the unlocked quests and complete it, and so on. For instance, let’s say that this game had only 4 quests: A, B, C, and D. Let’s say that after you complete • quest A, you unlock quests [B, D]. • quest B, you unlock quests [C, D]. • quest C, you unlock nothing [ ]. • quest D, you unlock quest [C]. Is this game winnable? Yes, because of the following scenario: The player picks quest A to start with. At the end of the quest A, the unlocked list contains [B, D]. Say that player chooses to do quest B, then the…
- The two friend Alpha and Beta have invented a new game called Coins&Papers. The game is played with their coins and a strip of paper divided into cells. The cells are numbered from the left, starting from 1. Alpha and Beta put some coins at some random cells on the strip, each coin in a cell. They alternatively take their turn to play the game. At each step, a player must take a coin and move it to a cell to the left of it. There is at most one coin in a cell at any time of the game. Of course, a coin cannot jump over another coin. Whoever cannot move loses the game. Beta takes her turn first. Develop a python code to find out who wins the game, if Beta could win the game, show her a winning move. If there are several winning moves, show her the winning move that uses the leftmost possible coin. If there are still several moves, show her the move that moves the coin as far as possible to the left. Sample Input: 1THIS MUST BE DONE IN CORAL: Cracked Egg Game: There are a dozen eggs in a basket; some are hard boiled and some are raw. The object of this game is for the user to guess the number of hard-boiled eggs prior to playing the game. The computer then simulates cracking all 12 eggs, using a random number 0 or 1 to simulate raw or hard boiled. The number 0 should represent raw eggs and the number 1 should represent hard boiled. The computer must keep track of the number of hard-boiled eggs. At the conclusion of cracking all 12 eggs, the actual number of hard boiled is compared to the user’s guess, and whether the user won or lost is given as output. The goal of this milestone is to use Coral to program one of the loops you will need for your finalized program in Project Two. This will help you define the logic, flow, and sequence of the game. For this work, you will write code in Coral for your selected programming game by accessing the activity in the zyBook. Note that links for each are…A video player plays a game in which the character competes in a hurdle race. Hurdles are of varying heights, and the characters have a maximum height they can jump. There is a magic potion they can take that will increase their maximum jump height by unit for each dose. How many doses of the potion must the character take to be able to jump all of the hurdles. If the character can already clear all of the hurdles, return . Example The character can jump unit high initially and must take doses of potion to be able to jump all of the hurdles. Function Description Complete the hurdleRace function in the editor below. hurdleRace has the following parameter(s): int k: the height the character can jump naturally int height[n]: the heights of each hurdle Returns int: the minimum number of doses required, always or more Input Format The first line contains two space-separated integers and , the number of hurdles and the maximum height the character can jump naturally.The…
- You have a maze with obstacles and non-zero digits in it: 9+ 7 8 + 4 1 2 3 4 5 You can start from any square, walk in the maze, and finally stop at some square. Each step, you may only walk into one of the four neighbouring squares (up, down, left, right) and you cannot walk into obstacles or walk into a square more than once. When you finish, you can get a number by writing down the digits you encounter in the same order as you meet them. For example, you can get numbers 9784, 4832145, etc. The biggest number you can get is 791452384, shown in the picture above. Your task is to find the biggest mumber you can get. Input There will be at most 25 test cases. Each test begins with two integers R and C (2 < R,C < 15, R+C < 30), the number of rows and columns of the maze. The next R rows represent the maze. Each line contains exactly C characters (without leading or trailing spaces), each of them will be either # or one of the nine non-zero digits. There will be at least one non-obstacle…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 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: