1.3-8. An urn contains 17 balls marked LOSE and three balls marked WIN. You and an opponent take turns select- ing a single ball at random from the urn without replace- ment. The person who selects the third WIN ball wins the game. It does not matter who selected the first two WIN balls. (a) If you draw first, find the probability that you win the game on your second draw. (b) If you draw first, find the probability that your oppo- nent wins the game on his second draw. (c) If you draw first, what is the probability that you win? HINT: You could win on your second, third, fourth, .., or tenth draw, but not on your .... first. (d) Would you prefer to draw first or second? Why?

A First Course in Probability (10th Edition)
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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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Can you help me understand part c of this? Thank you. 

 

Answer to a: 1/1140

Answer to b: 3/1140 or 1/380

 

1.3-8. An urn contains 17 balls marked LOSE and three
balls marked WIN. You and an opponent take turns select-
ing a single ball at random from the urn without replace-
ment. The person who selects the third WIN ball wins the
game. It does not matter who selected the first two WIN
balls.
(a) If you draw first, find the probability that you win the
game on your second draw.
(b) If you draw first, find the probability that your oppo-
nent wins the game on his second draw.
(c) If you draw first, what is the probability that you win?
HINT: You could win on your second, third, fourth, ..,
or tenth draw, but not on your
....
first.
(d) Would you prefer to draw first or second? Why?
Transcribed Image Text:1.3-8. An urn contains 17 balls marked LOSE and three balls marked WIN. You and an opponent take turns select- ing a single ball at random from the urn without replace- ment. The person who selects the third WIN ball wins the game. It does not matter who selected the first two WIN balls. (a) If you draw first, find the probability that you win the game on your second draw. (b) If you draw first, find the probability that your oppo- nent wins the game on his second draw. (c) If you draw first, what is the probability that you win? HINT: You could win on your second, third, fourth, .., or tenth draw, but not on your .... first. (d) Would you prefer to draw first or second? Why?
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