In a game, two coins are tossed. If either of the coins comesup heads, you have won a prize. To claim the prize, you must point toone of your coins that is a head and say 'look, that coin's a head, I'vewon'. You watch Fred play the game. He tosses the two coins, and hepoints to a coin and says 'look, that coin's a head, I've won'. What isthe probability that the other coin is a head?

Given, a game of tossing two coins.

Answered: In a game, two coins are tossed. If…

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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20 students from economics department were asked about their favourite course. 7 students said statistics, 3 of them said game theory, 9 of them said Microeconomics, 1 student said finance and 0 student said mathematics for economists. Draw a bar chart to represent the above information.(I have briefly shown you a bar chart during lecture. It’s nothing difficult but if you have any confusion, refer to the book or email me)
Three players enter a room and are given a red or a blue hat to wear. The color of each hat is determined by a fair coin toss. Players cannot see the color of their own hats, but do see the color of the other two players' hats. The game is won when at least one of the players correctly guesses the color of his own hat and no player gives an incorrect answer. In addition to having the opportunity to guess a color, players may also pass. Communication of any kind between players is not permissible after they have been given hats; however, they may agree on a group strategy beforehand. The players decided upon the following strategy. A player who sees that the other two players wear a hat with the same color guesses the opposite color for his/her own hat; otherwise, the player says nothing. What is the probability of winning the game under this strategy?
Solve the problem by deduction. Three chess players, Garry , Anatoly and Vishy competed for fun. Two of them won and one lost. Determine who won and lost by using the following clues:a. Anatoly won his match, if Garry lost his match.b. If Garry won his match, then Vishy lost his match.c. Anatoly lost his match, if Vishy won his match.
At a county fair, you pay $2 to play the following game: You are given a fair coin, and two bags standin front of you, labelled Bag A and Bag B. You flip a coin: If your coin lands Heads, you pick a ballfrom Bag A. If your coin lands tails, you pick a ball from Bag B. Each ball has a dollar value written onit, and you win the number of dollars shown on the ball. • Bag A contains four (4) balls in total: Three (3) balls show $1, and one (1) ball shows $5.• Bag B contains three (3) balls in total: Two (2) balls show $2, and one (1) ball shows $3.You WIN money if you leave with more money than you started with. You LOSE money if you leavewith less money than you started with. You BREAK EVEN if you leave with the same money that youstarted with.Let H denote the event that you flip heads, T denote the event that you flip tails, W the event that youwin, and L the event that you lose.(i) You pay to play exactly one game. What is the probability that you WIN given thatyou flipped a Heads?(ii)…
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Three students took a test. The professor comes and tells them that only one has passed the test.“Which is it?” they ask.“I can’t tell you that,” says the professor. “I can’t tell a student their own fate before the results are declared.”Student A takes the professor aside. “Look,” he says. “Of the three of us, only one has passed. That means that one of my fellow students is still sure to fail. Give me his name. That way you’re not telling me my own fate.”The guard thinks about this and tells him, “Student B has failed.”Student A rejoices that his own chances of passing have improved from 1/3 to 1/2. But how is this possible? The professor has given him no new information. Or has he?What do you think? Has the chances of student A risen from 1/3 to 1/2 and if so, why? Or does it still remain at 1/3 and if so, why? Can you specify what the initial chances were of each student passing/failing, and what their chances are after the profeesor ha shared the result for b
Player pays a fee, then reaches into a large jar and picks out a ball. The jar contains one ball for each letter of the alphabet. If the players picks out a ball with a vowel on it, the player wins 500 dollars. If the player picks out a ball with a consonant on it, the player wins nothing. What fee should be charged to play this game in order for it to be considered a fair game?
Two players play a game with the following rules: Player 1 puts on a blindfold while player two throws a die. The number that he gets is put aside as the "Target value". Then player two throws another die three times while giving player 1 information on weather he gets a lesser number than the target, equal to the target or greater than the target. Imagine that you are player one and you are handed the information that player two got [Lesser, equal, greater]. Deduce the probabilities of each possible target given the information.

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