Re: DSE 2011 A

Posted by Sinistral on May 11, 2013; 3:53am
URL: http://discussion-forum.276.s1.nabble.com/DSE-2011-A-a-request-to-duck-Amit-Sir-Q40-plz-tp7580464p7580587.html

first of all the solution to ques no 8 given in the very first post is wrong (as it is clear by reading the subsequent replies)

the right ans is in the 4th reply

to calculate how the game finishes in exactly 6 or exactly 7 matches, keep in mind that the game has to be stretched till the last match ==> the concerned player SHOULD win the LAST match AND he should have already won EXACTLY 3 of his previous matches (in this case 3 of his previous 5 or 6 matches)

for example calculating for x=6
5C3(1/2)^5: choosing 3 out of his previous 5 matches and winning those (& obviously losing the remaining)
1/2: probability of winning the last match.
2 : this can be done for both the players.

multiplying the above gives:
f(6)= 2* [5C3]*(1/2)^5   * (1/2)

similarly for f(7)

note that f(6)=f(7)