You WIN money if you leave with more money than you started with. You LOSE money if you leave with less money than you started with. You BREAK EVEN if you leave with the same money that you started with. Let H denote the event that you flip heads, T denote the event that you flip tails, W the event that and L the event that you lose. you win, You pay to play exactly one game. What is the probability that you WIN given that you (1) flipped a Heads? (ii) You pay to play exactly one game. What is the probability that you WIN? (iii) What are the expected winnings from playing one game?

Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter22: Frontiers Of Microeconomics
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You WIN money if you leave with more money than you started with. You LOSE money if you leave with
less money than you started with. You BREAK EVEN if you leave with the same money that you started
with.
Let H denote the event that you flip heads, T denote the event that you flip tails, W the event that
and L the event that
you win,
you
lose.
(i)
flipped a Heads?
You pay to play exactly one game. What is the probability that you WIN given that you
(ii)
(iii)
You pay to play exactly one game. What is the probability that
you WIN?
What are the expected winnings from playing one game?
Transcribed Image Text:You WIN money if you leave with more money than you started with. You LOSE money if you leave with less money than you started with. You BREAK EVEN if you leave with the same money that you started with. Let H denote the event that you flip heads, T denote the event that you flip tails, W the event that and L the event that you win, you lose. (i) flipped a Heads? You pay to play exactly one game. What is the probability that you WIN given that you (ii) (iii) You pay to play exactly one game. What is the probability that you WIN? What are the expected winnings from playing one game?
At a county fair, you pay $2 to play the following game: You are given a fair coin, and two bags stand in
front of you, labelled Bag A and Bag B. You flip a coin: If your coin lands Heads, you pick a ball from Bag A.
If your coin lands tails, you pick a ball from Bag B. Each ball has a dollar value written on it, 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.
Transcribed Image Text:At a county fair, you pay $2 to play the following game: You are given a fair coin, and two bags stand in front of you, labelled Bag A and Bag B. You flip a coin: If your coin lands Heads, you pick a ball from Bag A. If your coin lands tails, you pick a ball from Bag B. Each ball has a dollar value written on it, 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.
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