Suppose I play a gambling game where I either win or lose k dollars. Suppose furtherthat the chance of winning is p = .5.I employ the following strategy to try to guarantee that I win some money.I bet $1; if I lose, I double my bet to $2, if I lose I double my bet again. I continue untilI win. Eventually I'm sure to win a bet and net $1 (run through the first few rounds andyou'll see why this is the net).If this really worked casinos would be out of business. Our goal in this problem is tounderstand the flaw in the strategy.(a) Let X be the amount of money bet on the last game (the one I win). X takes values1, 2, 4, 8, .... Determine the probability mass function for X. That is, find p(2k), where kis in {0, 1, 2,...}.(b) Compute E(X).(c) Use your answer in part (b) to explain why the stategy is a bad one.

Answered: Image /qna-images/answer/2838e18f-2ba7-420e-a1f2-884e2390d688.jpg

Answered: Suppose I play a gambling game where I…

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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Solve the problems below using the "Tree Diagram" strategy. You are one of the goalkeepers in your soccer team but today's game depends who is the Coach today...with Coach Sam the probability of being Goalkeeper is 0.5 or with Coach Alex the probability of being Goalkeeper is 0.3 Sam is Coach more often than Alex... about 6 out of every 10 games (a probability of 0.6). So, what is the probability you will be a Goalkeeper today?
You may want to create a table to help you with this problem. Consider a computer test to indicate if you like Math 123 or dislike Math 123. If positive, you like the class and if negative you dislike the class. In a sample of 25 thousand people, 80% of the population indicated they liked the class. If the test is 85.5% accurate, what are the chances that the test showed the person disliked Math 123, but in reality they actually liked the course? Round your percentage to 2 decimals.
(4) You are a contestant on a television game show and you have won $5000 so far. You are now offered a choice: either you can keep the money and leave or you can continue into the next round. where you have a 70% chance of increasing your winnings to $10000 and a 30% chance of losing the $5000 and finishing the game with nothing. (a) Which option would you choose? (b) How does your choice compare with that which would be prescribed by the expected monetary value criterion? b) As the decision tree below shows, according to the EMV criterion you should continue to the next round because your expected winnings, at $7000, are higher than your current winnings of $5000. Winnings (3) 5000 Keep the money Continue to ned 70001 0.7 Increase winnings Lose 0.3 10 000 0
c) A manufacturer is considering the production of a new and better mousetrap. She estimates the probability that the new mousetrap is successful is ¾. If it is successful, it would generate profits of $174,000. The development costs of the mousetrap are $121,000. Should the manufacturer proceed with plans for the new mousetrap? Why or why not?
Charlie buys a one-year term home insurance policy for $p, that will pay $200,000 in the event of a major catastrophe and $35,000 in the event of a minor catastrophe. Charlie's home has a 0.2% chance of a major catastrophe and a 0.7% of a minor catastrophe during the one year term. What did the insurance company charge Charlie for this policy if the company expected to break even?
After giving the lotto a try you decide to go back to Clayton Campus for some more gambling action. Theyare playing a die tossing game where you win a brand new home if you roll all sides of the die within 7rolls. Your crystal ball can see into the future and tells you that when you roll the die 7 times you don't seethe same number appear twice in a row. You decide to bet your entire rent for the year and try to win thehouse. You toss a fair six-sided die 7 times. Consider the following events, A = “each value appears atleast once” and B = “the outcome is alternate in numbers (i.e., a specific face of the die cannot be observed to occur directly after it was observed on the previous roll but it may have occurred elsewhere inthe sequence of rolls)”. What is p(A|B)? Are you likely to win the house?
A lawyer, considering taking a case figures that there is a two and five chances of winning the case in the court and earning his firm $400,000, a two and five chances of losing and costing his firm $250,000, and a one and five chances of settling out of court and bringing in $200,000. Should the lawyer take the case based on his expected payoff? explain using mathematical argument.
If you were charged $8.00 to play this game, you would on average see a ..... (lose/gain) of ...... per spin.
An option to buy a stock is priced at $150. If the stock closes above 30 next Thursday, the option willbe worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20and 30, the option will be worth $200. A trader thinks there is a 50% chance that the stock will closein the 20-30 range, a 20% chance that it will close above 30, and a 30% chance that it will fall below20. a) Create a valid probability table.b) How much should the trader expect to gain or lose?c) Should the trader buy the stock? Why?
Answer the following question. In a recent competition, each of three teams played each other team once. The results are given in the table below. What was the score of the A vs. C game? Give A's goals first. Team A B C Wins 1 1 0 Losses Ties 0 1 0 1 2 0 Goals For Goals Against 6 3 2 4 2 5 (Remember: Your solution must show appropriate work or reasoning.)

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