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 Tennis,anyone? (Posted on 2010-09-07)
As a condition for the acceptance to a tennis club a novice player N is set to meet two members of the club, G (good) and T (top, i.e. better than good) within a total of three games (i.e. at most three!).
In order to be accepted, N must win against both G and T in two successive games.
N is free to choose with whom to start: T or G.
Which one is preferable?

Attributed to the late Leo Moser (1921—1970)

 See The Solution Submitted by Ady TZIDON Rating: 5.0000 (1 votes)

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 solution | Comment 1 of 7

perhaps my reasoning is wrong, but according to my determinations it does not matter which he chooses to play first.

My reasoning is as follows:
Let Gw,Gl represent a win/loss against G and
Tw,Tl a win/loss against T

Now if he plays G first then the possible paths to acceptance are
Gw,Tw
Gw,Tl,Tw
Gl,Gw,Tw

now if instead he plays T first then the paths to acceptance are
Tw,Gw
Tw,Gl,Gw
Tl,Tw,Gw

now these are just permutations of the 3 paths for playing G first, thus when you compute the probabilities for each path they are the same.  Thus the overall odds of acceptance are the same regardless of who he plays first.
if G is the odds of winning against G and T against T then the overall odds of accceptance are
GT+G(1-T)T+(1-G)GT

 Posted by Daniel on 2010-09-07 11:47:01

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