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ps: probability [#permalink] New post 06 Apr 2005, 10:31
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john tried to solve the following question using this formula:
4C2(1/2)^3(1/2)=3/16. what's the flaw in his logic?
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 [#permalink] New post 06 Apr 2005, 10:49
1/4

all outcomes=8
possible outcomes=2

2/8+2/8=2/8 or 1/4

i dont understand john`s logic ?
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Last edited by christoph on 06 Apr 2005, 22:25, edited 1 time in total.
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 [#permalink] New post 06 Apr 2005, 13:21
I don't think it is useful to use formulas in this case
total possible outcomes are 2^4=16
you can have 3 consecutive tails in 3 ways:
TTTH
TTTT
HTTT
same for heads
so 6/16
hope it's correct
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 [#permalink] New post 06 Apr 2005, 14:09
1/8.
first could be heads or tails, the remaining three have 1/2 probability to be heads, if the 1st is tails and viceversa.

So, 2 out of 16 have desired results = 1/8.
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 [#permalink] New post 06 Apr 2005, 14:42
Let us suppose the game ends on 4th throw.

So it could be

HTTT ----(1)

or TTTH------(2)

(1) could be achieved in 4C3(1/2)^3*(1/2)

(2) could be in 4C3(1/2)^4

Add the above two

4*(1/16) + 4*(1/16)= 8/16 = 1/2

So probablility of chances of the game finishing after 4th chance is
1-1/2 = 1/2
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 [#permalink] New post 06 Apr 2005, 19:33
But if the first three are heads, or tail, then there wouldn't be a fourth throw (correct me if i am wrong)
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 [#permalink] New post 06 Apr 2005, 21:59
Folaa3 wrote:
But if the first three are heads, or tail, then there wouldn't be a fourth throw (correct me if i am wrong)


thats what I think

so it should be only when :

THHH
or HTTT

what is the OA?
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 [#permalink] New post 06 Apr 2005, 22:32
christoph wrote:
1/4

all outcomes=8
possible outcomes=2

2/8+2/8=2/8 or 1/4

i dont understand john`s logic ?


all outcomes=16
possible=2 =>HTTT or THHH
=>1/16+1/16=2/16=1/8
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 [#permalink] New post 07 Apr 2005, 08:53
Probability that it will end at the third throw:
2/2^3=1/4
Probability that it will end at the fourth throw:
2/2^4=1/8

Probability that it will end after the fourth throw:
1-1/4-1/8=5/8
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 [#permalink] New post 07 Apr 2005, 08:57
we don't have 2 answers matching :roll:
OA?
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 [#permalink] New post 07 Apr 2005, 09:01
It doesn't matter if one answer matches with other people's answer. Look at the logic of the answer. Is the logic right?
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 [#permalink] New post 07 Apr 2005, 09:06
HongHu wrote:
It doesn't matter if one answer matches with other people's answer. Look at the logic of the answer. Is the logic right?


I agree with your logic because I used the same one but I didn't understand the language and instead of 1-3/8 I just thought 3/8 (see above!)

However, I just wanted to say that the more we have different answers, the more I look forward to knowing the correct one!
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 [#permalink] New post 07 Apr 2005, 09:23
Ahh I see. The question asks the possibility of ending the game after the fourth throw. You gave the possibility that the game would end before or at the fourth throw.
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  [#permalink] 07 Apr 2005, 09:23
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