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 leave with less money than you started with. You BREAK EVEN if you
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.
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
win, and L the event that you lose.
(i) You pay to play exactly one game. What is the probability that you WIN given that
you flipped a Heads?
(ii) You pay to play exactly one game. What is the probability that you WIN?
(in) What are the expected winnings from playing one game?
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