An unfair coin is flipped. If a head turns up, you win $1. If a tail turns up, you lose $1. The probability of a head is 0.56and the probability of a tail is 0.44. What is the expected value of the game?wwwLet X be the random variable for the amount won on a single play of this game. Fill in the probabilities for theprobability distribution of the random variable X.X $1 $-1P₁(Type integers or decimals.)

Suppose a variable X defines the amount won on a single play of the game.

Answered: An unfair coin is flipped. If a head…

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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Hector plays a game with a friend. They pay $2 and roll a 6-sided die. If the die comes up a 3 or higher, they win $7. If it doesn't, they win nothing. What is the expected value of the game? Give your answer to the closest cent (two decimal places).
You roll five fair six-sided dice. Let X denote the sum of the numbers shown. Compute the expectation and the variance of X.
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $15. If you roll a 3, 4 or 5, you win $1. Otherwise, you pay $10. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table X P(X) b. Find the expected profit. $ (Round to the nearest cent) c. Interpret the expected value. This is the most likely amount of money you will win. O If you play many games you will likely lose on average very close to $0.33 per game. O You will win this much if you play a game. d. Based on the expected value, should you play this game? O No, this is a gambling game and it is always a bad idea to gamble. O Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. O Yes, because you can win $15.00 which is greater than the $10.00 that you can lose. O Yes, since the expected value is 0,…
Show your work . Justify an answer
If the probability distribution for the random variable X is given in the table, what is the expected value of X? Xi - 5 1 5 Pi .3 .5 .2 LO
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Your friend Phil, asks you what you think about a new scratch-off lottery game. It costs $10 to play this game, There are two outcomes for the game (win, lose) and the probability that a player wins a game is 60%. A win results in $15, for a net win of $5 ($15 minus the $10 paid to play). The probability distribution for x� (the amount of money a player wins or loses) in a single game is as follows:
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $9. If you roll a 3, 4 or 5, you win $2. Otherwise, you pay $3.a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table X P(X) b. Find the expected profit. $ (Round to the nearest cent)c. Interpret the expected value. You will win this much if you play a game. If you play many games, on average, you will likely win, or lose if negative, close to this amount. This is the most likely amount of money you will win. d. Based on the expected value, should you play this game? No, this is a gambling game and it is always a bad idea to gamble. Yes, because you can win $9.00 which is greater than the $3.00 that you can lose. No, since the expected value is negative, you would be very likely to come home with less money if you played many games. Yes,…
Your friend convinces you to play a game where you roll a standard die one time. It costs $5 to play the game. If you roll a 3 or a 4 you win $9. Any other roll wins nothing. 4. Find the expected value of this game.
Oscar is playing a simple card game. The game is played by the player picking a card from a deck. If the player picks any face cards, they wins $20. If the player picks any other cards, they lose $10. Let X be the random variable representing the $ amount Oscar will win/ lose from this game. (a) Fill in the probability distribution of X. Leave the probability as a fraction. X P(X) Win $ Lose $ (b) Calculate the expected value of X. Round your answer to the nearest hundredth of a dollar. (for example if the answer is 43.5478, then round to 43.55). The expected value is $
Suppose that you are offered the following "deal." You roll a six sided die. If you roll a 6, you win $17. If you roll a 2, 3, 4 or 5, you win $4. Otherwise, you pay $6. a. Complete the PDF Table. List the X values, where X is the profit, from smallest to largest. Round to 4 decimal places where appropriate. Probability Distribution Table P(X) b. Find the expected profit. $ (Round to the nearest cent) c. Interpret the expected value. O This is the most likely amount of money you will win. Oif you play many games you will likely win on average very close to $4.50 per game. O You will win this much if you play a game. d. Based on the expected value, should you play this game? O No, since the expected value is negative, you would be very likely to come home with less money if you played many games. O Yes, since the expected value is positive, you would be very likely to come home with more money if you played many games. O No, this is a gambling game and it is always a bad idea to gamble.…

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