You are a contestant on a game show. There are three closed doors in front of you. The game show host tells you that behind one of thesedoors is a million dollars in cash, and that behind the other two doors there are trashes. You do not know which doors contain which prizes,but the game show host does.The game you are going to play is very simple: you pick one of the three doors and win the prize behind it. After you have made yourselection, the game show host opens one of the two doors that you did not choose and reveals trash. At this point, you are given the option toeither stick with your original door or switch your choice to the only remaining closed door.To maximize your chance to win a million dollars in cash, should you switch?Choices:A) YesB) NoC) It doesn't matter because the probability for you to win a million dollars in cash stays the same no matter if you switch or not.

As per the question we are given the famous "monty hall problem" which we have to logically solve.…

Answered: You are a contestant on a game show.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Maria plays the following game: There is a jar containing 2 gold coins, 2 silver coins, and 6 bronze coins. She must select two coins. She gets $2 for each gold coin she selects. She gets $1 for each silver coin she selects. She gets nothing for selecting bronze coins. For example, if she picks one gold and one silver coin, she will get $3 total. If she picks one silver and one bronze coin, she gets $1 total. Let X be her winnings for this game. Fill in the pmf table (leave your answers here as fractions). x 0 1 2 3 4 p(x) Compute the expected value. Write your answer as a decimal (as you would a dollar amount): $ .
In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side. The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is this a fair game. = Win a prize = Do not win a prize 1. Start by determining the probabilities for winning a prize and not winning a prize. Draw a probability tree to find the possible outcomes and the probabilities. After you draw the tree, check you work by clicking on the link below. Click to hide hint CHIP 1 CHIP 2 Probability P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25 0.5 0.5 0.5 P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25 Start 0.5 0.5 P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25 0.5 P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25
Logan and his children went into a restaurant and where they sell drinks for $3 each and tacos for $2 each. Logan has $35 to spend and must buy at least 12 drinks and tacos altogether. If Logan decided to buy 5 drinks, determine all possible values for the number of tacos that he could buy. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Bob and Tom are graduating and are no longer going to be roommates, but they both want to keep the dog they adopted. Using the Method of Sealed Bids, Bob bids $285 and Tom bids $433 for the dog. Since Tom's bid is higher, he gets the dog. How much will he have to pay Bob in order to keep the division fair?
Miguel is playing a game in which a box contains four chips with numbers written on them. Two of the chips have the number 1, one chip has the number 3, and the other chip has the number 5. Miguel must choose two chips, and if both chips have the same number, he wins $2. If the two chips he chooses have different numbers, he loses $1 (–$1). Let X = the amount of money Miguel will receive or owe. Fill out the missing values in the table. (Hint: The total possible outcomes are six because there are four chips and you are choosing two of them.) Xi 2 –1 P(xi) What is Miguel’s expected value from playing the game? Based on the expected value in the previous step, how much money should Miguel expect to win or lose each time he plays? What value should be assigned to choosing two chips with the number 1 to make the game fair? Explain your answer using a complete sentence and/or an equation. A game at the…
If you live in Dallas, then you live in Texas. Greg lives in Dallas. No conclusion Greg lives in Dallas. Greg lives in Texas. Greg is a Cowboy's fan.
For his Carnival project, Chester designed a game where players pick a random marble from a bag. In the bag there are 2 pink marbles, 10 green marbles, and 8 white marbles. If players draw a pink marble they get a large candy bar prize, if they draw a green marble they get a small lollipop prize, and if they draw a white marble they get a fist bump. Chester purchased a set of 16 candy bars for $12 and a bag of 200 lollipops for $20. Answer the following questions: What is Chester's expected cost per game? $ If Chester plans for 40 people to play his game, How many candy bars should he expect to give out? How many lollipops should he expect to give out?
Dave and Frank are graduating and are no longer going to be roommates, but they both want to keep the cat they adopted. Using the Method of Sealed Bids, Dave bids $247 and Frank bids $493 for the cat. Since Frank's bid is higher, he gets the cat. How much will he have to pay Dave in order to keep the division fair?
Carl was competing on a game show, and he ran into a losing streak. First, he bet half of his money on one question and lost it. Then he lost one fourth of his remaining money on another question. Then he lost $300 on another question. Then he lost two-thirds of his remaining money on another question. Finally, he got a question right and won $200. At this point, the show ended, and he had $800 left. How much did he have before his losing streak began?
You and two friends decide to go to a casino and play Blackjack. You find an empty table and sit down. The dealer shuffles and deals from a new 52 card deck. In order to win, you and your friends know that you need to either score a 21 (blackjack and automatic win) or get a higher total than the dealer. You know that a deck of cards has 13 different cards (2-10, Jack, Queen, King, and Ace), and that there are 4 copies of each in the deck. You know that an ace is equal to either 1 or 11 and that Jacks, Queens, and Kings are worth 10. The dealer deals out the following cards: You: Jack and Ace Friend 1: King and 10 Friend 2: 10 and 10 Dealer: 10 and ? The dealer is about to deal their last card. What are the following probabilities: A) What is the probability that the next card can beat your hand? B) What is the probability that the next card can tie your hand? C) What is the probability that the next card can beat your friends?
A carnival game has 160 rubber ducks floating in a pool. The person playing the game takes out one duck and looks at it. If there's a red mark on the bottom of the duck, the person wins a small prize. If there's a blue mark on the bottom of the duck, the person wins a large prize. Many ducks do not have a mark. After 50 people have played the game, only 3 of them have won a small prize, and none of them have won a large prize. Estimate the number of the 160 ducks that you think have red marks on the bottom. Then estimate the number of ducks you think have blue marks. Explain your reasoning.
To raise money for the local Veterans Affairs hospital, your friend organizes a fundraiser, inviting you to play a two-stage game where you pay $8 to play. The game works as follows: a fair 8-sided die is rolled, noting the number shown, and a spinner divided into 4 equal regions of different colors (blue, red, green, orange) is spun, noting the color. If the die shows 3 or the spinner shows orange, then you win $21. If the die shows an even number and the spinner does not show orange, then you win $9. Otherwise, you do not win anything. Let X be your net winnings. (a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact. X P(X) (b) Compute your expected net winnings for the game. Round your answer to the nearest cent. $ (c) Is this game fair? Yes No

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