A game is said to be fair if the expected value (after considering the cost) is 0. This would mean that in the long run, both the player and the "house" or whoever is putting on the game, would expect to win nothing. If the value is positive, the game is in your favor. If the value is negative, the game is not in your favor. At a carnival, you pay $1 to choose a card from a standard deck. If you choose a red card you double your money, but if you pick a black card you do not get any. (A standard deck of cards has 52 card. 26 of the cards are red.) • E • •• • ••2 14444244 144 2 +t * + + +* • 2 • • • • 1. Complete the probability distribution below. P(x) Color of card x → Net Money Won or Lost Red + $ 24 Black Click to view hint 2. What is the expected value?

A game is said to be fair if the expected value (after considering the cost) is 0. This would mean that in the long run, both the player and the "house" or whoever is putting on the game, would expect to win nothing. If the value is positive, the game is in your favor. If the value is negative, the game is not in your favor. At a carnival, you pay $1 to choose a card from a standard deck. If you choose a red card you double your money, but if you pick a black card you do not get any. (A standard deck of cards has 52 card. 26 of the cards are red.) • E • •• • ••2 14444244 144 2 +t * + + +* • 2 • • • • 1. Complete the probability distribution below. P(x) Color of card x → Net Money Won or Lost Red + $ 24 Black Click to view hint 2. What is the expected value?

Name: Sta6.Fair Games and Expected Value: Game 1ngedstA game is said to be
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Sta6.Fair Games and Expected Value: Game 1ngedstA game is said to be fair if the expected value (after considering the cost) is 0. This would mean that in the longrun, both the player and the "house" or whoever is putting on the game, would expect t

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...

See similar textbooks

Similar questions

Suppose I flip a fair coin n = 20 times. A psychic tries to predict the outcome before each flip. Three researchers have different ideas about the psychic's ability. There is Sydney, the Skeptic (S), who thinks the psychic's success rate is between 49% and 51%. There is Morgan, the Mark, M, who thinks that the psychic's success rate is 80%. And there is Carter, the Cynic (C), who thinks the psychic's success rate is 10%. Specifically: S+ 0 ~ U(.49, .51) M + 0 = .80 C0 = .10 %3D In all cases, assume the number of successful predictions follows a binomial distribution with success rate 0. Usek for the number of successes and n for the number of trials. Given all that: Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Carter over Morgan. Call that Bayes factor Bc:M Determine the formula for the Bayes factor (a.k.a., likelihood ratio) supporting Morgan over Sydney. Call that Bayes factor BM:S Determine the formula for the Bayes factor (a.k.a., likelihood…
Zara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game. Note: Sue only rolls a die once. The second roll, if the game goes up to that point, is made only by Zara.
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?.
# A surgery has a success rate of 75%. Suppose that the surgery is performed on three patients. a) what is the probability that the surgery is successful on a lest 2 patients? b) on average, how many surgeries can we expect to be successful if performed on a group of three patients? c) what is the standard deviation of the number of successful surgeries performed on a group of three patients?
At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1–4), noting the number showing. If the die shows a 3 and the coin shows tails, then you win $22. If the coin shows heads and the die shows an even number, 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.
Chandler offers you the opportunity to play his $2 game where he shuffles four cards and you must pick the correct one. What is the expected profit per person if the prize is a $1.25 coke for the game?Single line text.
One option in a roulette game is to bet $7 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 $7 you paid to play the game and you are awarded $7. If the ball lands elsewhere, you are awarded nothing and the $7 that you bet is collected. Complete parts (a) through (b) below. III a. What is the expected value for playing roulette if you bet $7 on red? $ (Round to the nearest cent.) b. What does this expected value mean? Choose the correct statement below. O A. This value represents the expected loss over the long run for each game played. OB. Over the long run, the player can exper to break even. OC. This value represents the expected win over the long run for each game played.
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.)
Suppose it costs $29 to roll a pair of dice. You get paid 4 dollars times the sum of the numbers that appear on the dice. What is the expected payoff of the game? Is it a fair game? The expected payoff of the game is $? is it a fair game?
The player pays a fee of $5 to play. The player then rolls a 12-sided die three times. If the player rolls a 7 on any of the three rolls, they win a prize. The prize is determined by the number of 7s rolled. If the player rolls one 7, they win $5. If the player rolls two 7s, they win a $10. If the player rolls three 7s, they win $20. Compare the theoretical results of the game to the experimental results, including a discussion of whether the results were typical or rare. Theoretical results: Roll (including all 3 rolls) Result Money earned 1 7,7,7 $15 2 2,4,5 $5 3 5,7,9 $5 4 1,9,3 $0 5 2,12,7 $5 6 3,12,3 $0 7 7,4,8 $5 8 6,7,7 $10 9 5,12,4 $0 10 7,5,7 $10 Experimental results: Roll (including all 3 rolls) Result Money earned 1 1,3,7 $5 2 3,6,4 $0 3 7,6,9 $5 4 8,7,7 $10 5 11,4,1 $0 6 6,5,7 $7 7 4,6,3 $0 8 7,1,9 $7 9…
A casino game with cards takes $1 bets. Gamblers have a 46% chance to win back their bets plus $1, and they have a 54% chance of losing their bets. Can you evaluate the house edge for thisgame, if so please explain.