Practice 2. The Monty Hall Problem is a probability puzzle originally posed by Steve Selvin.It is loosely based on the game show Deal or No Deal and is named after its host, MontyHall. The problem is as follows.Suppose you're on a game show, and you're given the choice of three doors: Behind one dooris a car; behind the others, goats. You pick a door, say No. 1, and the host, who knowswhat's behind the doors, opens another door, say No. 2, which has a goat. He then saysto you, "Do you want to pick door No. 3?" Is it to your advantage to switch your choice?(Whitaker, 1990, as quoted by vos Savant 1990a)For i = 1, 2, 3, let C₁ = {the car is behind the ith door} and O₁ = {Monty opens the ith door}.(a) Assuming you picked the first door, find P(C₁ | O₂) and P(C3 | O₂), and then comparethe two probabilities. Is it to your advantage to switch your choice?

The Monty Hall problem is a classic example of conditional probability. To analyze the problem, we…

Answered: Practice 2. The Monty Hall Problem is a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Reuben is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random. This game is this: Reuben rolls the number cube once. He wins $1 if a 1 is rolled, $2 if a 2 is rolled, and $3 if a 3 is rolled. He loses $2.50 if a 4, 5, or 6 is rolled. (If necessary, consult a list of formulas.) (a) Find the expected value of playing the game. | dollars (b) What can Reuben expect in the long run, after playing the game many times? O Reuben can expect to gain money. He can expect to win dollars per roll. O Reuben can expect to lose money. He can expect to lose dollars per roll. O Reuben can expect to break even (neither gain nor lose money).
A firm making production plans believes there is a 30% probability the price will be $10, a 50% probability the price will be $15, and a 20% probability the price will be $20. The manager must decide whether to produce 6,000 units of output (A), 8,000 units (B) or 10,000 units (C). The following table shows 9 possible outcomes depending on the output chosen and the actual price. Production $10 $15 6,000 (A) -$200 $400 8,000 (B) -$400 $600 10,000 (C) -$1,000 $800 If the mean-variance rule is used, how much should the firm produce? Multiple Choice O 6,000 8,000 Profit (Loss) when price is $20 $1,000 $1,600 $3,000 10,000 cannot use this rule to make the decision X
In a history class, Colin and Diana both take a multiple choice quiz. There are 10 questions. Each question has five possible answers. What is the probability that: a) Colin will pass the test if he guesses an answer to each question? b) Diana will pass the test if she studies so that she has a 75% chance of answering each question correctly?
A particular gambling game pays 4 to 1 and has a 20% chance to win. Someone will bet $10, 125 times, and keep track of the total amount won or lost. Which of the following boxes will produce the right answers? Check ALL answers that apply. a. 1 ticket labeled $10 and 4 tickets labeled -$10 b. 20 tickets labeled $10 and 80 tickets labeled -$10 c. 20 tickets labeled 1 and 80 tickets labeled 0 d. 1 ticket labeled $40 and 4 tickets labeled -$10 e. 20 tickets labeled $40 and 80 tickets labeled -$10 f. 1 ticket labeled 1 and 4 tickets labeled 0
Use this spinner game to answer questions 1 - 3. It costs $10 to play this game. The pointer is on blue. Probability Pay out Amount +1 $0 $8 $5 $15 $20 $18 Number of sectors: 6 Blue 20.00% -1 Pink 15.00% Number of spins: 1 Gray 30.00% Orange 10.00% Number of spins so far: 0 Green 12.00% Red 13.00% What would the owners expected profit or loss be from this game? Give your answer with a dollar sign and include a negative sign out front if needed. Do not round.
Many casinos have a game called the Big Six Money Wheel, which has 54 slots in which are displayed a Joker, the casino logo, and various dollar amounts, as shown in the table at the top of the next column. Players may bet on the Joker, the casino logo, or one or more dollar denominations. The wheel is spun and if the wheel stops on the same place as the player's bet, the player wins that amount for each dollar bet. Denomination Number of slots $40 (Joker) 1 $40 (Casino logo) 1 $20 2 $10 4 $5 7 $2 15 $1 24 If a player bets $4 on the $10 denomination, find the player's expectation. (Round your answer to two decimal places.)
What theorems and principles are employed to solve the following riddle: Ten band members have had their musical instruments placed randomly within boxes. Each band member gets five shots at opening boxes, trying to find their own instrument. (Thus, a 50% chance of each individual finding the desired instrument.) They're not allowed to communicate about what they find. If the entire band fails to find their instruments, they're all fired...and the odds of them all finding their instruments via random guessing is 1 in 1,024. But the drummer has an idea that will radically increase their odds of success. What theorems and principles would you need to employ to solve the riddle. Solving the riddle is not the question. What are the methods (proof by contraposition, would be an example) Rules :• Instruments have been randomly placed in 10 boxes.• The pictures on the boxes don't necessarily correspond to the instruments inside.• Each musician can open up to 5 boxes, and they have to…
. A small-town carnival has a simple game that you can play with a number cube. If you roll a 6 you win a fluffy teddy bear. If you roll a 1, 2, 3, 4, or 5 you get a piece of stale gum. After watching other children play the game 50 times, only 2 children have won a teddy bear. You decide to simulate the game with a random number table. a) Determine labels for your outcomes. b) Using the random number table below, determine how many times a “6” appears in 50 trials. c) What percentage of a “6” in 50 trials did you get from the simulation? d) What percentage of a “6” did you observe at the carnival? e) How do your answers for parts (c) and (d) compare? What does this tell you about the

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