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While you are waiting for your nets to fill, you play the following game: you have two coins, one is fair (heads/tails with equal probability), one is biased (heads twice as likely as tails). The coins are otherwise identical. You are going to choose a coin at random, flip it N many times, and then try to decide based on the results whether the coin is the fair coin or the biased coin. You win the game if you correctly identify the coin. (Your robot cat is able to distinguish which coin is which, and scores the game.)
You decide to follow the following strategy: if the majority of the flips are heads, you’ll guess it is the biased coin, otherwise you’ll guess that it is fair. That is, you’re setting a threshold of N/2 such that if you get that many heads or more, you guess it is the biased coin, otherwise you guess it is the fair coin.
1) Following this strategy, what’s the probability you win in a game of 10 flips? 20 flips?
2) If you want to maximize your probability of winning, what threshold should you set for your strategy in a game
of 10 flips? 20 flips? Be thorough as to your methods, and precise.
jkhl hlkha sd d dsd fjk k;jl jl l;k j;klj j;jl lk j;kl lk
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- A high school has 1000 students and 1000 lockers, one locker for each student. On the first day of school, the principal plays the following game: She asks the first student to open all the lockers. She then asks the second student to close all the even-numbered lockers. The third student is asked to check every third locker. If it is open, the student closes it; if it is closed, the student opens it. The fourth student is asked to check every fourth locker. If it is open, the student closes it; if it is closed, the student opens it. The remaining students continue this 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 the game is over, the program will output the number of lockers and the lockers numbers of the…Jack and Jill will play a game called Hotter, Colder. Jill chooses a number from 0 to 100, and Jack makes repeated attempts to guess it. For each guess, Jill will respond with: hotter - if the current guess is closer to her number than the previous guess is colder - if the current guess is farther to her number than the previous guess is same - if the current guess is as far (to her number) as the previous guess is For Jack’s first guess, since there is no previous guess yet, Jill will just answer same. Describe an algorithm or a systematic approach that Jack can follow to win the games faster (fewer guesses). Example: Jill chooses number 40. Note: Jack can guess any number from 0 to 100 at any point of the game. Jack guesses 100. Jill responds same (first guess) Jack guesses 60. Jill responds hotter (60 is closer to 40 than previous guess 100) Jack guesses 80. Jill responds colder (80 is farther from 40 than previous guess 60) Jack guesses…EXERCISE - You go to a market to pick out some gourds to decorate your house for Halloween. The market has a special October deal where you get 3 randomly chosen gourdss for $10. Each gourd can either be an orange pumpkin, a green pumpkin or a squash. The probabilities for picking each one of them are: P(orange pumpkin) = 0.6, P(green pumpkin) = 0.3, and P(squash) = 0.1. A: What is the probability that the first gourd is an orange pumpkin, the second is a green pumpkin, and the third is a squash? B: What is the probability that you get all 3 as orange pumpkins? C: What is the probability that you get no squashes? D: What is the probability that you get at least one orange pumpkin? (ANSWERE USING PYTHON)
- he Dice game of “Pig” can be played with the following rules. Roll two six-sided dice. Add the face values together. Choose whether to roll the dice again or pass the dice to your opponent. If you pass, then you get to bank any points earned on your turn. Those points become permanent. If you roll again, then add your result to your previous score, but you run the risk of losing all points earned since your opponent had rolled. Continue to roll as much as you want. However, once a “1” comes up on either die, your score is reduced to 0, leaving you only with points that you have previously "banked." Furthermore, you must pass the dice to your opponent. The first person to 100 points is the winner. When a player rolls two dice, the possible outcomes are as follows: Die #2 Roll Roll a 1 Roll a 2 Roll a 3 Roll a 4 Roll a 5 Roll a 6 Die #1 Roll Roll a 1 0 0 0 0 0 0 Roll a 2 0 4 5 6 7 8 Roll a 3 0 5 6 7 8 9 Roll a 4 0 6 7 8 9 10 Roll a 5 0 7 8 9 10 11 Roll a 6 0 8 9 10…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.Imagine playing a number guessing game. A side is a number from 0 to Nhe's holding it, and the other side is trying to find that number by taking turns guessing. Number-holding side estimatehe has to offer one of the following three options in response to the party that did it:1-Your guess is correct, you found the number I kept (Game Over).2-Your estimate is wrong, but you are closer to the correct estimate than the previous estimate.3-the wrong estimate and the correct estimate are further away than the previous estimate.To find the estimated number in an environment where all the information is these, astrategy will be followed: Make a prediction (N/2) from the exact middle of N with 1 Begin:Find out the answer to your guess. [answer=answer_ogren (guess)]If the answer is equal to 1, the game is over, you can leave.If the answer is equal to 2, you are going in the right direction, keep the forecast direction;If you're heading for small numbers, the new N is now N/2.Make a guess…
- Q1. Let’s play a dice game with a pair of dice following these rules:1. At the beginning, you throw a pair of dice. If the two numbers add up to 5, 6, 7, 8, or 9, thegame immediately stops.2. If your first throw does not meet those 5 totals, you would continue until you get either 11 or12.Get 1000 simulations of this paired dice game. What is the average number of dice throw per game?You can use the sample() function to simulate the dice.Problem 1. You are playing a version of the roulette game, where the pockets are from 0 to 10and even numbers are red and odd numbers are black (0 is green). You spin 3 times and add up the values you see. What is the probability th at you get a total of 17 given on the first spin you spin a 2? What about a 3? Solve by simulation and analytically.A group of people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After x number of passes, the person holding the hot potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. For example: number of passes = 1 and number of players = 5, the order of elimination is 2, 4, 1, 5. Write a program for general values of X and N. Ask a user for the number of people and number of passes To speed up the input and debugging, you may wish to store the names of the people in a file. Make sure no two names start the same letter ( Alex and Ana are not OK). Alternatively, you can number the players. Output number and/or the name of a person being eliminated Output number and the name of the winner Do not expect a user to do the right thing, error check the user input; among other things, what do you think a reasonable…
- A spinner with three equal sections is being used in a game. One section is labeled “0 points,” and two sections are labeled “2 points.” A player can decide not to spin the spinner and score 1 point. Each player gets one turn, and the player with the higher score wins; in case of a tie, the winner is decided by one flip of a fair coin. Alex takes his turn first. Eddie, knowing Alex’s score, takes his turn next. If both players use strategies that maximize their winning probabilities, what is the probability that Alex wins? a 1/3 b 1/2 c 2/3 d 4/9There are 7 balls hidden in a box (3 blue and 4 green). If you first select a green ball and do not replace in the box, what is the probability that the second ball you select from the box will also be green? [Your answer can be written either as a fraction or decimal]A group of people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After x number of passes, the person holding the hot potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. For example: number of passes = 1 and number of players = 5, the order of elimination is 2, 4, 1, 5. Write a program for general values of X and N. Ask a user for the number of people and number of passes To speed up the input and debugging, you may wish to store the names of the people in a file. Make sure no two names start the same letter ( Alex and Ana are not OK). Alternatively, you can number the players. Output number and/or the name of a person being eliminated Output number and the name of the winner Do not expect a user to do the right thing, error check the user input; among other things, what do you think a reasonable…