DSE 2006 Q31-33

[Mauli]

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/24_june_2006_option_a.pdf

someone else had also posted the same doubts and duck had told to find the attachment in the earlier posts.
i couldnt find the thread.
i found a thread regarding these doubts but the contents had been deleted.
please help.

[Prerna Rakheja]

Hi Mauli,

Ques 31.
Case 1) A wins the first match:
==> AA + ACBAA + ACBACBAA + ACBACBACBAA +... = 2/7

Case 2) A loses the first match:
==> BCAA + BCABCAA + BCABCABCAA + ... = 1/14

Therefore, probability that A wins the contest is 2/7 + 1/14 = 5/14

where, AA indicates A wins the first match and the second match. ACBAA indicates A wins the 1st match, C wins the 2nd match B wins the 3rd match and so on.

Ques 32.
 Case 1) A wins the first mtach:
==> ACC + ACBACC + ACBACBACC +... = 1/7

Case 2) B wins the first match:
==> BCC + BCABCC + BCABCABCC + ... = 1/7

Probability that C wins the contest = 1/7 + 1/7 = 2/7

Ques33.

Case 1) A wins the first match:
==> ACBACBACB.. = 1/2^infinity

Case 2) B wins the first match:
==> BCABCABCA.. = 1/2^infinity

Probability that the game is never ending = 1/infinity + i/infinity = 0

[Sinistral]

I think Duck already answered this question . You even thanked her

http://discussion-forum.2150183.n2.nabble.com/duck-please-see-this-tp7582206p7582284.html

[Mauli]

thanks prerna:)

[Mauli]

yeah i know sinistrial .
i had posted this way b4 my request to duck .
its a sheer coincidence that both the replies have come around at the same time .
:D