My answer yesterday gave a qualitative answer but no mathematics to
back it up. Here it is:
Let G1 be the girl who picks first, G2 the girl who picks second, etc.
Let P(Gn) be the probability that the nth girl picks the right number.
Then:
P(G1) = 1/10 (trivial)
P(G2) = 9/10 * 1/9 = 1/10 The probability that G2 will pick the number
is the probability G1 won't pick the number (9/10) times the
probability G2 will pick the number if G1 doesn't (1/9).
P(G3) = 9/10 * 8/9 * 1/8 = 1/10 The probability that G3 will pick the number
is the probability G1 won't pick the number (9/10)
times the probability G2 won't pick the number if G1 doesn't (8/9)
times the probability G3 will pick the number if G1 and G2 don't (1/8).
.
.
etc.
So by the pattern you can see that every girl will have a 1/10 chance of
guessing the right number.
Glenn
gmbbradford@netscape.net (Glenn Bradford) wrote:
>Oops,
>Changed my mind. The game is fair either way. The advantage a later girl
>gets by knowing some wrong answers is offset by some girl preceding her
>that guesses it right.
>Glenn
>
>gmbbradford@netscape.net (Glenn Bradford) wrote:
>
>>GJ,
>>It depends on whether or not the father is thinking up a (possibly) new
>>number before each girl's guess. If he isn't, the girl who complained is
>>justified. If he is, the game is fair, and this could explain his look of
>>befuddlement.
>>Glenn
>>
>>"G. Peeters" <gjpeeters@wish.nl> wrote:
>>>The birthdayparty
>>>
>>>During the birthdayparty of her daughter, a father takes a chololate bar and
>>>shows it to the ten girls that are standing in front of him.. He says, "I
>>>will think of a number between 1 and 10. (1 and 10 included) Whoever guesses
>>>the number is the winner of this chocolate bar.. Jane.. You may start"
>>>Jane - al excited - says "Four"
>>>"Well.. I'm sorry, but that is wrong" father replies
>>>Marie says "Nine!"
>>>"Also wrong" father says.
>>>Annie says "Two"
>>>And again it is wrong. Then one of the girls says "I don't think this game
>>>is played right this way.. I don't think we girls have an even chance of
>>>winning.. What if you are the girl that is the last to say a number?" The
>>>girl says
>>>
>>>Father looks bewildered.. not knowing how to reply...
>>>
>>>Well... is the girl right? Do all the girls have an even chance of winning?
>>>
>>>---
>>>
>>>
>>>Now I will 'really' go on vacation... Have fun with this one..
>>>C U in three weeks..
>>>
>>>Gert-Jan
>>>
>>>
>>>
>>>
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>>
>>
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>
>
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