9. Consider a gamble based on a toss of a fair coin: you pay ¥x and then toss thecoin. If the toss results in a "head", you get 2x, but if it results in a "tail", youget nothing. Suppose you have ¥200 in total and can make the bets in one oftwo ways. You can either bet the entire ¥200 on a single toss, or you can bethalf of your money on the first toss and the remaining half on the second toss.(a) If you are risk-averse, which way would you prefer? You may assumeu(0) = 0.(b) If you are risk-neutral, which way would you prefer?

We have to answer question based on decision theory.

Answered: 9. Consider a gamble based on a toss of…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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You draw a card from a deck of 52 cards. If the card is a spade, you win $5, but if the card is not a spade you lose $2.What is your expected earning from this game?
A pair of fair dice is rolled onoe, Suppose that you lose $7 if the dice sum to 5 and win $8 if the dice sum to 11 or 12. How much should you win or lose if any other number tums up in order for the game to be fair? To keep the game fair, you should (Do not round until the final answer. Then round to the nearest cent as needed.) if the dice sum to any other number
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.)
If I $6 to play a spinner game and the chances of winning $1 dollar is 50% and the chances of winning $12 is 50%. What is the fair price of the game?
A friend proposes a gamble to you. You roll 2 fair, six-sided dice, and add up the results of each die to find your total number. If your roll totals a 6 or 8, your friend pays you $30. If you roll any other total, you pay your friend $10. What is your expected payoff from playing this game 100 times?.
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…
If someone were to bet $1 on the second dozen numbers (which pays 2 to 1) in the game of roulette 33 seperate times, what is the chance that they would end up losing money?
Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws three twos in succession from a standard deck of 52 cards without replacement, you give him $100. Otherwise, he pays you $10. If the same bet was made 25 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary. Answer Кeypad Keyboard Shortcuts O Win O Lose %24
A certain game involves tossing 3 fair coins, and it pays 11¢ for 3 heads, 7¢ for 2 heads, and 4e for 1 head. Is 7¢a fair price to pay to play this game? That is, does the 7¢ cost to play make the game fair? .... The 7¢ cost to play a fair price to pay because the expected winnings are (Type an integer or a fraction. Simplify your answer.)
2. Two people have different opinions on the Tennessee and Florida game to be played tonight. One person supports Tennessee and is willing to offer 11 to 10 odds; the other person supports Florida and is willing to offer 5 to 3 odds. Go through the analysis to determine how much to bet with each person. If Heili has $100 to invest, how much is she assured of earning?
A roulette wheel has 38 numbers, with 18 odd numbers (black) and 18 even numbers(red), as well as 0 and 00 (which are green). You bet 5 dollars that the outcome is anodd number. If you win you get 10 dollars; otherwise you lose your 5 dollars. Note:assume the 0 and 00 numbers are considered even numbers What is your expected winnings? Which of these options is best: bet on an odd number or don’t bet? Why?

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