Somebody tosses a fair coin and if the result is heads, you get nothing, otherwise you get $5. How much would you pay to play this game? What if the win is $500 instead of $5?
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- Sabrina is on a game show and is presented with a drawer containing 10 red socks, 10 blue socks, 10 green socks, and 10 yellow socks. Sabrina is to take socks out of the drawer and put them in a bag. She will win $1 for every sock she puts in the bag, as long as the bag does not contain 5 or more socks of one color and 5 or more socks of another color. For example, if she takes 5 red, 4 blue, 3 green, and 2 yellow socks, she would win $14. However, if she took 5 red, 5 blue, 3 green, and 2 yellow socks, she would not win anything because there are two colors (red and blue) that have 5 or more socks each. What is the most money that Sabrina can win? Enter your answer as a single integer only (no words, no dollar signs). A/ What is the minimum number n such that if n socks are removed from the drawer and put into a bag, that the bag will necessarily contain at least 5 socks of one color and at least 5 socks of another color? Enter n as a single integer, no words.Children often play the game of rock, paper, and scissors. This game has two players, each of whom chooses one of the three objects: rock, paper, or scissors. If player 1 chooses rock and player 2 chooses paper, player 2 wins the game because paper covers the rock. The game is played according to the following rules: If both players choose the same object, this play is a tie. If one player chooses rock and the other chooses scissors, the player choosing the rock wins this play because the rock breaks the scissors. If one player chooses rock and the other chooses paper, the player choosing the paper wins this play because the paper covers the rock. If one player chooses scissors and the other chooses paper, the player choosing the scissors wins this play because the scissors cut the paper. Write an interactive program that allows 1 person to play this game against the computer. Input This program has two types of input: The users’ responses when asked to play the game. The…This is related to Dungeons and Dragons: Your character has just been reduced to 0 Hit Points (HP) (because of a fireball) and is now dying. They must now make several Death Saving Throws to determine their fate. Death saving throws are rolled every turn until you get three successes or three failures. To make a death saving throw, simply roll a d20. If the roll is 10 or higher, you succeed. Otherwise, you fail. On your third success, you become stable. On your third failure, you die. If you roll a 1, it counts as two failures. If you roll a 20, you regain 1 hit point. In which case, you regain consciousness and can fight once more! Calculate the probability that your character dies.
- 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…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…Send the solution on paper Q3:\ There's a simple game you can play with silver dollars. (A silver dollar is a coin worth $1). There are five (5) silver dollars on the table and you and your opponent take turns picking up 1, 2, or 3 coins until none is left. You get to keep each silver dollar you pick up. But, if you pick up the last coin, you have to pay $2 to your opponent. The object of the game is to finish with the most money. Consider building a game tree to solve the above problem where each state in the game tree represents the number of coins left on the table. - What utility function should you use to evaluate terminal nodes? - Your opponent offers to let you go first. • If you accept, what is your first move? How much will you earn? • Should you accept? Briefly explain your answer.
- You are given $500 to start the game.Every time you spin the wheel you have a chance of:S - Splitting your money in half.P - Plunging to zero. (You lose.)I - Increasing your money to double.N - Never needing money again! (You win!)You may quit at any time and go home with your current winnings.Current winnings = $500 - SPIN? (Y/N) ySPINNING . . .S - winnings will be split in halfCurrent winnings = $250 - SPIN again? (Y/N) ySPINNING . . .I - winnings will be increased by doubling you current winningsCurrent winnings = $500 - SPIN again? (Y/N) ySPINNING . . .I - winnings will be increased by doubling you current winningsCurrent winnings = $1000 - SPIN again? (Y/N) ySPINNING . . .I - winnings will be increased by doubling you current winningsCurrent winnings = $2000 - SPIN again? (Y/N) ySPINNING . . .N - never need money againYOU WIN!!!Total winnings = $1000000000 - thanks for playing!You have a pack of 5 randomly numbered cards, which can range from 0-9. You can win if you can produce a higher two-digit number from your cards than your opponent. Return true if your cards win that round. Examples winRound ([2, 5, 2, 6, 9], [3, 7, 3, 1, 2]) → true // Your cards can make the number 96 // Your opponent can make the number 73 // You win the round since 96 > 73 winRound ([2, 5, 2, 6, 9], [3, 7, 3, 1, 2]) → true winRound ([1, 2, 3, 4, 5], [9, 8, 7, 6, 5]) → false winRound ([4, 3, 4, 4, 5], [3, 2, 5, 4, 1]) → falseA 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 4/9
- 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.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)In a game called NIM, there are two players. At the start, two piles of matches are placed on the table in front of them, each containing two matches. In turn, the players take any (positive) number of matches from one of the piles. The player taking the last match loses. Which player is sure to win in this game? O First Player O No answer text provided. O There is no way of knowing the outcome. O Second Player