**Game Rules and Analysis**You are allowed to play a game with the following rules. You pay $1 to flip a fair Quarter, Nickel, and Dime. If they all three come up Heads or all three come up Tails, you get $3. You are allowed to play this as many times as you want.**Tasks:**A. Create a Table to go through the Probabilities for the outcomes (win or lose).B. What is the Expected Value of playing this game?C. Should you play this game?---**Explanation for Educational Website:****Potential Outcomes:**1. All coins come up Heads.2. All coins come up Tails.3. Mixed results (not all Heads or all Tails: any combination of Heads and Tails in different orders).**Probabilities:**- Probability of all Heads (HHH) = $ \frac{1}{8} $ - Probability of all Tails (TTT) = $ \frac{1}{8} $- Probability of Mixed results = $1 - \left(\frac{1}{8} + \frac{1}{8}\right) = \frac{6}{8}$ or $ \frac{3}{4} $**Win/Loss Table:**| Outcome | Probability | Winnings | Net Gain/Loss ||-----------|-------------|----------|---------------|| All Heads or All Tails | $ \frac{2}{8} $ or $ \frac{1}{4} $ | $3 | $2 || Mixed Results | $ \frac{6}{8} $ or $ \frac{3}{4} $ | $0 | -$1 |**Expected Value Calculation:**\[ \text{Expected Value} = \left(\frac{1}{4} \times 2\right) + \left(\frac{3}{4} \times (-1)\right) \]\[ = \frac{1}{2} - \frac{3}{4} \]\[ = -\frac{1}{4} \]The expected value of playing this game is $-\frac{1}{4}$, meaning you are expected to lose 25 cents per game on average.**Conclusion:**Considering the negative expected value, it is not advisable to play this game if you aim to make a profit

3 coin : One coin= 2 outcomes (H or T) H= Head T=Tail Possible outcomes : 2³ = 8…

Answered: 2. You are allowed to play a game with…

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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Similar questions

Deals with comparing probabilities, answer correctly.
You're playing a dice game where you pay $1 to play, you win $1 if you roll an even number and lose a $1 if you roll an odd number. What's the expected value of the game?
Suppose you are invited to play a game in which you bet $1 on any number from 000 to 299. If your number comes up, you get $75. Find the expected winnings. Expected winnings = $ (Type an integer or decimal rounded to the nearest cent as needed.)
You draw and keep a single bill from a hat that contains a $1, $10, $20, and $50 bill. What is the expected value of the game to you?
Finding Odds in Roulette A roulette wheel has 38 slots. One slot is 0, another is 00, and the others are numbered 1 through 36, respectively. You place a bet that the outcome is an odd number. a. What is your probability of winning? b. What are the actual odds against winning? c. When you bet that the outcome is an odd number, the payoff odds are 1:1. How much profit do you make if you bet $18 and win? d. How much profit would you make on the $18 bet if you could somehow convince the casino to change its payoff odds so that they are the same as the actual odds against winning? (Recommendation: Don’t actually try to convince any casinos of this; their sense of humor is remarkably absent when it comes to things of this sort.)
You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $48 or $60 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) $48 $48 $48 0.125 $48 $48 $60 0.125 $48 $60 $48 0.125 $48 $60 $60 0.125 $60 $48 $48 0.125 $60 $48 $60 0.125 $60 $60 $48 0.125 $60 $60 $60 0.125 The expected price paid is ______ . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders would not be willing to bid against each other. The probabilities of the…
You are on a TV show. You have been asked to either play a dice game four times or accept a $50 bill. Thedice game works like this:If you roll a 1, 2, you lose $30. If you roll a 3, 4 or 5, you win $100. If you roll a 6, you lose $50.Should you play the game? Answer yes or no.__________ Use expected values and decision theory to justify your answer. Please round the answer to two decimal places.Expected value of four games is $__________.
Brandon is setting up his own carnival game. His plan is to make sure that the game has a negative expected value, because that will be the most beneficial for his own profit. He decides to set the following rules. You pay $10 to play, and then you get to throw one dart at a dartboard. The dartboard is broken up into 8 equally sized sections. 3 of the sections are red. 4 of the sections are blue. 1 of the sections is green. If your dart hits the green section, Brandon hands you $30. If your dart hits any of the red sections, he gives you $15. If your dart hits any of the blue sections, you win nothing. What is the expected value for one turn? (Just write the number rounded to the nearest thousandths without the dollar sign. ie. 0.123 or -0.123)
One option in a roulette game is to bet $28 on red. (There are 18 red compartments, 18 black compartments, and two compartments that are neither red nor black.) If the ball lands on red, you get to keep the $28 you paid to play the game and you are awarded $28. If the ball lands elsewhere, you are awarded nothing and the $28 that you bet is collected. Find the expected payback for this roulette game if you bet $28 on red.
A bag of marbles contains 2 gold marbles, 10 silver marbles, and 30 black marbles. You decide to play the following game: Randomly select one marble from the bag. If it is gold, you win $5. If it is silver, you win $2. If it is black, you lose $2. What is the expected value if you play the game? Express losses as negative values and do not include the dollar sign in your answer. Round to the nearest cent. Provide your answer below:
Hector plays a game with a friend. They have a bag which contains 13 red stones and 3 black stones. They pay $1 and pull out a stone. If the stone is black, Hector wins $6. If the stone is red, Hector wins nothing.. What is the expected value of the game?
You are on a TV show. You have been asked to either play a dice game five times or accept a $120 bill. The dice game works like this: If you roll a 1 or 5, you win $50. If you roll a 4, you win $150. If you roll a 2, 3 or 6, you lose $30. Should you play the game? Answer yes or no. __________ Use expected values and decision theory to justify your answer. Please round the answer to two decimal places. Expected value of five games is $__________

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