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urgent math help

the question is -  A fully booked theatre is about to screen A Beautiful Mind to a group of 100 mathemati- cians. the 1st mathematican was thinking about the Riemann Hypothesis and somehow misplaced his ticket. As a consequence, he could not find the seat alloted to him and decided to sit at a random seat. From then on, any mathematician if he finds his seat oc- cupied, politely goes and seats at a random seat. What is the probability that the 100th mathematician seats in his own seat?

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1 Answer

Funny but interesting question.
 
The key to this is to realize that two events are possible
 
1)Riemann guy sits in his correct seat
2)Riemann guy does not sit in his correct seat
 
P1=1/100
P2=99/100
P100: Probability that 100th guy gets correct seat
 
If(P1), then P100=100% since everyone finds his correct seat
 
If(P2), then P100=1/99 since it will be a random chance that P100 will get his correct seat.
 
Using conditional probability
 
P100=P1*1 + P2*(1/99)=.01 + 99/100*1/99)=0.021
P100=2%
 
1: I'm not 100% confident with this, but it feels correct.  Even if Riemann guy fails, there is still a chance that the others will fail to find the 100th guys' seat.
 
Update!
 
This has been bugging me all day.  I think the answer is closer to 50% after further thought.  I started with 2 seats and added an additional seat to work through the sample spaces.  It is not uniformly 50% independent of #seats, but approaches this answer asymptotically.  Still working on it ;-)   Nice problem!!
 
Final Answer: I'm convinced - the answer is 50% regardless of how many seats - excellent problem.

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sir can u solve this question for me
 Imagine you are playing a new version of the game of chess, called Pravega chess. the rules are same, with just one exception. You have to play 2k moves at a time, where k is any natural number. Prove that, black who plays second always has a non-losing strategy.

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