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appears. Somewhat surprisingly player 2 has a considerable advantage in this
game. No matter what player 1 picks, player 2 can win with probability 2/3.
Suppose without loss of generality that player 1 picks a pattern that begins
with H:
case
1
2
3
4 Player 1
HHH
HHT
HTH
HTT Player 2
THH
THH
HHT
HHT Prob. 2 wins
7/8
3/4
2/3
2/3 Verify the results in the table. You can do this by solving six equations in six
unknowns but this is not the easiest way.
1.61. At the New York State Fair in Syracuse, Larry encounters a carnival
game where for one dollar he may buy a single coupon allowing him to play a
guessing game. On each play, Larry has an even chance of winning or losing a
coupon. When he runs out of coupons he loses the game. However, if he can
collect three coupons, he wins a surprise. (a) What is the probability Larry will
win the surprise? (b) What is the expected number of plays he needs to win or
lose the game.
1.62. The Megasoft company gives each of its employees the title of programmer (P) or project manager (M). In any given ye...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).
 Spring '10
 DURRETT
 The Land

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