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Probability Problem
by Ravi Sharma - Monday, 12 September 2011, 03:22 PM
  Please help me with this problem

In 1896 lord Coin has decided to play a game. From the January 1 till December 31 every day he chooses among two match boxes an arbitrary one and placed a match from it to another box (if the chosen box was not empty). If the chosen box was empty then he placed a match from
the other box to the chosen one. What is the probability that after the December 31 the both boxes will have an equal number of matches if at the beginning each box had a) n = 400 b) n = 200 c) n = 100 matches?
Re: Probability Problem
by R Maanav - Thursday, 29 September 2011, 10:51 PM

The year 1896 is a leap year. For the match boxes to have equal no. of match sticks after 31st december 2011, i.e. the 366th day, it is necessary that Lord Coin choose each match box equal no. of times.

Hence the ans. should be (366 C 183)*((1/2)^183)*((1/2)^183), i.e., (366 C 183)((1/2)^366))

irrespective of the initial no. of match sticks in each match box. What is the answer by the way?