2. Explain the Monte Hall Paradox with aContingency Table.The Monte Hall Paradox comes from the Morning Game Show "Let's Make a Deal" whichused to be shown right before the "Price is Right" 5 days a week. Monte Hall was thename of the Host. For the final deal there are 3 doors labeled, Door #1, Door #2, andDoor #3 (yes that is what they were called). One of the three doors was a Grand Prizeand behind the other two doors was nothing. The Contestant would pick one of thedoors, for the purpose of this problem (let's say they picked Door #1). Then Monte Hallwould open one of the losing doors, (let's say Door #2 just to keep it simple). Now theContestant has a choice, they can stay with their choice (in our Example Door #1) orchange to the remaining door (in this case Door #3). The Paradox is that the remainingdoor (in our example Door #3) actually is the door with the Grand Prize 2/3 of the time.Explain why it's not 1/2.

So as we know that the monte hall paradox has three doors. One of which has a grand prize. The…

Answered: 2. Explain the Monte Hall Paradox with…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.CR: Chapter 12 Review

Problem 92CR

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Two cars are meeting at an intersection and want to proceed as indicated by the arrows in the figure below. Each player can proceed or move. If both proceed, there is an accident. A would have a payoff of -100 in this case, and B a payoff of -1000 (since B would be made responsible for the accident, sinceA has the right of way). If one yields and the other proceeds, the one yielding has a payoff of -5, and the other one of 5. If both yield, it takes a little longer until they can proceed, so both have a payoff of -10. Analyze this simultaneous game by drawing the payoff matrix, and find any pure and mixed strategy Nash equilibrium.
Suppose that you and a friend are playing cards and decide to make a bet. If you draw three twos in succession from a standard deck of 52 cards without replacement, you win $100. Otherwise, you pay your friend $10. If the same bet was made 25 times, how much would you expect to win or lose?
5. Mr. Bernard and Mr. Meyer go out to lunch and play a game called "One Hundred". Each player puts $50 in an envelope. Then, Mr. Bernard goes first, and the players take turns choosing numbers between one and nine. On cach turn, the new number chosen is added to the previous total. The player who can bring the total to exactly $100 wins all the money. In games like this, there is often a first-move advantage or a second-move advantage. If both Mr. Bernard and Mr. Meyer play optimally, who should end up winning this game? Explain your reasoning. Hint: start at the end of the game and work backwards toward the start of the game! a. b. Identify the optimal strategies (complete plans of action) for each player?
Suppose that there is a negotiation between two players over a painting. Person 1,the seller ,has no interest in the painting. On the other hand the painting is worth $100 to the buyer. If the painting is sold at a price in between 0 and 100, both are better off. Player 1 proposes a price p to player 2. Then after observing player 1's offer, player decides whether to accept it or to reject it. If the offer is rejected both zero and the game ends.Find the unique SPNE of this game.
Consider the game of Let’s Make a Deal in which there are three doors (numbered 1, 2, 3), one of which has a car behind it and two of which are empty (have “prizes”). You initially select Door 1, then, before it is opened, Monty Hall tells you that Door 3 is empty (has a prize). You are then given the option to switch your selection from Door 1 to the unopened Door 2.
4. On a game show, you start with a prize pool of $1 000 000, but before you get it, you must answer trivia questions. Every time you get a question wrong, the current prize pool is cut in half, and you must keep answering questions. The game ends when you get a question right and you receive whatever is left of the prize pool. (For example, if you get the first two questions wrong, the prize pool is cut in half twice, so it becomes $250 000. If you then get the third question right, you go home with $250 000 as your winnings.) (a) If you have a chance of getting each question right, what is the distribution of Q: the total number of questions you have to answer? (Give the name of the distribution and its parameters.) (b) Express the amount of money you win as a function of Q. (c) Find the expected amount of money you win.
Mike and Bill play a card game with a standard deck of 52 cards. Mike selects a card from a well-shuffled deck andreceives A dollars from Bill if the card selected is a diamond and receives $1 from Bill if the card selected is an ace that is not adiamond. Otherwise, Mike pays Bill two dollars. Determine the value of A if the game is to be fair.
James placed a $25 bet on a red and a $5 bet on the number 33 (which is black) on a standard 00 roulette wheel. -if the ball lands in a red space, he wins $25 on his 'red' but loses $5 on his '33' bet - so he wins $20 -if the ball lands the number 33, he loses $25 on his 'red' bet but wins $175 on his '33' bet: He wins $150 -if the ball lands on a spae that isn't red and isnt 33 he loses both bets, so he loses $30 So for each spin; he either wins $150, wins $20, or loses $30 -probability that he wins $150 is 1/38 or .0263 -probability that he wins $20 is 18/38 or .4737 -probability that he loses $30 is 19/38 or .5000 let X = the profit that james makes on the next spin x P (X=x) x*P(X=x) x^2*P(X=x) 150 .0263 3.945 591.75 20 .4737 9.474 189.48 -30 .5000 -15.000 450.00 sum (sigma) 1.000 -1.581 1231.23 u (expected value)= -$1.581 variance = 1228.73044 standard deviation = 35.053 FILL IN THE BLANK if you play 2500 times, and Let, x (x bar)= the mean winnings (or…
The following are the rules of the game: One player is chosen to be the "It" that guards the preso (empty can). The rest of the players are the hitters, and each throws the pamato (slipper) to the toe-line to topple down the preso. If a player throws the farthest from the toe-line, he/she becomes the "It". The hitters are divided between the two opposite sides. When the hitters run out of throwing objects, the game translates into a chase. Players on one side will act as bait while those on the other side will try to kick the can to avoid being tagged. R2: R3: R4: R5: R6: Given the set of rules of the game, answer the following: 1. Identify the simple statements, compound statements, and the connectives involved in compound statements. Explain your answer. 2. Make a twist in the game by adding a new rule to the game or replacing one of the rules of the game.
A new game is being introduced at the Hard Rock Cafe. A ball is spun around a wheel until it comes to rest in one of many spots. Whatever is listed in that spot will be the player's winnings. If the wheel has 7 spots labeled $1, 9 spots labeled $2, and 9 spots labeled $10, how much should a player expect to win on average?
This problem is courtesy of Mr. Lange’s friend Paul. The Queen of Hearts is a card game played at a local club. Participants purchase raffle tickets at $5 apiece, and one raffle ticket is chosen at random. The participant whose raffle ticket is selected will then select an envelope containing a card from a standard deck with two jokers. If the card selected is between a 2 and a 5 inclusive, the participant collects $20. If the card selected is between a 6 and a 9 inclusive, the participant collects $30. Any ace, 10, jack, or king pays $40, each joker pays $75, and the queens of diamonds, clubs, and spades each pay $100. The queen of hearts pays the jackpot, hence the game’s name. Suppose there are three cards remaining, the queen of hearts, the queen of diamonds, and the queen of clubs. Also suppose the jackpot pays $35000. Mr. Lange wishes to purchase 400 of the 1600 tickets sold in a given night. Answer the following questions: (a) What is the probability that Mr. Lange has the…
3. A coworker offers you the following deal. For a $10 fee, you may pick an envelope from a box containing 100 seemingly identical envelopes. However, each envelope contains a coupon for a free gift. • Ten of the coupons are for a free gift worth $6. • Eighty of the coupons are for a free gift worth $8. • Six of the coupons are for a free gift worth $12. • Four of the coupons are for a free gift worth $40. a. Define the random variable.

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