airnessOver the holidays, many families sit down and play games together. So did my family.One evening, my family played a game that heavily relied on luck. Imagine we playeda game that used rolling six-sided dice (as in the game Monopoly) and the outcomeof ones turn was based on the result of rolling the dice. My son made three bad rollsin a row and yelled “This is unfair!". Elaborate whether he was right or wrong withhis statement.. Use only what we discussed about fairness in this lecture.

Answered: airness Over the holidays, many…

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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the carnival has come to town, and lucky louie has once again set up his pavilion. He offers a simple game consisting of rolling two normal six-sided dice at the same time for the extraordinarily low price of $3.00 per play. If the player rolls a sum of 3, the player wins $13.00; if the sum is a 9, the player wins $9.00; and if the sum is a 12, the player wins $12.00. Otherwise, the player does not win anything. How much should you expect to win or lose per game (after paying the $3.00) ?
Suppose you roll 2 dice. What is the pobability that the sum of the 2 dice is exactly 8, given that the 1st dice is a 5? Please explain how to get the answer
When throwing the dice, if the number of points shown is 1,2,3, he wins 200 dinars, and if the number of points is 4.5, he loses 300 dinars, but if he gets the point 6, he wins 600 dinars, the amount expected to earn this person from this game is 200 true Error
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?
What are the possible outcomes if you roll out 3 dice at the same time?
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…
In a game, two coins are tossed. If either of the coins comes up heads, you have won a prize. To claim the prize, you must point to one of your coins that is a head and say 'look, that coin's a head, I've won'. You watch Fred play the game. He tosses the two coins, and he points to a coin and says 'look, that coin's a head, I've won'. What is the probability that the other coin is a head?
You have been asked to play a card game. A card is dealt from a complete deck offifty-two cards (no jokers). A deck has 4 aces, 4 kings, 4 queens, 4 jacks, and 36 other cards.It works like this:• If the card is a ace, you lose $4.• If the card is a king or jack, you lose $10.• If the card is a queen, you win $8.• If the card is anything else, you win $1.Find the expected value of the game. Write the excepted value rounded to the nearest cent
A child rolls 7 standard dice of different colors and records the numbers showing. Find the number of different outcomes
Emma and Eddie both want to choose their family's dinner entrée. Emma prefers burgers, and Eddie would like to order pizza. To determine who gets to pick, their dad suggests rolling a pair of fair dice. If the sum of the dice is 4 or 10, then Emma will pick dinner. If the sum is 2, 3, 11, or 12, then Eddie will pick dinner. They will roll the dice again if any other number is rolled. Is this a fair way to decide? Explain.(Hint: There are 21 total possibilities when rolling a pair of dice.) a No, it is not fair because there is a higher probability of rolling 2, 3, 11, or 12, so Eddie will most likely choose dinner. b Yes, it is fair because both Emma and Eddie have an equal probability of choosing dinner. c No, it is not fair because there is a higher probability of rolling 4 or 10, so Emma will most likely choose dinner. d No, it is not fair because there is a greater probability that they will roll a number other than 4, 10, 2, 3, 11, or 12.
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?
In the board game Clue, the object of the game is to determine the which character is the murderer, whichweapon was used and in which room the murder took place (e.g., “Colonel Mustard with the Candlestickin the Library”). There are 6 different characters, 6 weapons, and 9 rooms. How many different outcomesare possible?

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