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  M15 #31 [#permalink]
New postPosted: Mon Oct 20, 2008 4:17 am 
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John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fourth throw?

(A) \frac{1}{16}
(B) \frac{2}{16}
(C) \frac{3}{16}
(D) \frac{4}{16}
(E) \frac{6}{16}

[Reveal] Spoiler: OA
B

Source: GMAT Club Tests - hardest GMAT questions


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  Re: M15 #31 [#permalink]
New postPosted: Sun Dec 05, 2010 12:16 pm 
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My solution:
1st throw - we don't care tail of head. Prob is 1
2nd -4th throws - we need 3 consequitive items, which are opposite to item in 1st throw. Therefore, cumulative probability is 1/2*1/2*1/2 = 1/8

It took me 20 sec to find the correct asnwer which is 2/16= 1/8


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  Re: GMATClub M15: Probability [#permalink]
New postPosted: Mon Oct 20, 2008 6:00 am 
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is d ans b....

1/16 + 1/16

2/16


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  Re: GMATClub M15: Probability [#permalink]
New postPosted: Mon Oct 20, 2008 6:26 am 
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scthakur wrote:
John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fourth throw?
a. 1/16
b. 2/16
c. 3/16
d. 4/16
e. 6/16

Correct answer is B.


Tricky question!! good one.

this trap for 4/16 (answer D).

TOTAL no. of ways. = 2^4=16

At the first look we may thought all below four combinations are correct.
HTTT
THHH
TTTH -- If this were the case game would have been over after 3 throws.
HHHT-- If this were the case game would have been over after 3 throws.


so only two possiblilites...
ans = 2/16

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  Re: GMATClub M15: Probability [#permalink]
New postPosted: Mon Oct 20, 2008 9:51 am 
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x2suresh wrote:
scthakur wrote:
John throws a coin until a series of three consecutive heads or three consecutive tails appears. What is the probability that the game will end after the fourth throw?
a. 1/16
b. 2/16
c. 3/16
d. 4/16
e. 6/16

Correct answer is B.


Tricky question!! good one.

this trap for 4/16 (answer D).

TOTAL no. of ways. = 2^4=16

At the first look we may thought all below four combinations are correct.
HTTT
THHH
[color=#BF0000]TTTH -- If this were the case game would have been over after 3 throws.
HHHT-- If this were the case game would have been over after 3 throws.[/color]

so only two possiblilites...
ans = 2/16



Nice explanation Suresh. I could not imagine the highlighted part and ended up selecting 4/16 as the answer.


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  Re: M15 #31 [#permalink]
New postPosted: Tue Sep 22, 2009 7:26 am 
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nice explanation, got tricked by this Q. :)

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  Re: M15 #31 [#permalink]
New postPosted: Mon Nov 30, 2009 1:33 pm 
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ohh snapp this is a tricky one. I got the right answer in abt 15 sec but it took me over a minute to realize the trap of 4/16. i went over my answer abt 5 times thinking it was wrong. i really have to spend more time on looking at answer choices before i start cramping the maths. :x


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  Re: M15 #31 [#permalink]
New postPosted: Tue Dec 01, 2009 9:07 am 
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  Re: M15 #31 [#permalink]
New postPosted: Tue Dec 07, 2010 8:15 am 
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I said E.........DUMB MISTAKE!! I rushed it and forgot about the "consecutive" part.


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  Re: M15 #31 [#permalink]
New postPosted: Tue Dec 07, 2010 2:34 pm 
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Vorskl wrote:
My solution:
1st throw - we don't care tail of head. Prob is 1
2nd -4th throws - we need 3 consequitive items, which are opposite to item in 1st throw. Therefore, cumulative probability is 1/2*1/2*1/2 = 1/8

It took me 20 sec to find the correct asnwer which is 2/16= 1/8


Your reasoning is wrong since you do care what is the first throw - if it is H and then you get 2 more Hs the game ends. You got the correct answer by chance. Though, chance is also a factor in this test.

EDIT: I now see that you wrote: "which are opposite to item in 1st throw." so i guess it is correct.


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  Re: M15 #31 [#permalink]
New postPosted: Wed Dec 08, 2010 7:14 am 
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B.

Two possibilities for this to occur:
THHH
HTTT

For both the prob of each event needs to be multiplied as they are dependent events:
Hence 1/2 * 1/2 * 1/2 * 1/2
=1/16
for both events multiply by 2 =>
2 * 1/16 = 2/16


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  Re: M15 #31 [#permalink]
New postPosted: Fri Dec 09, 2011 7:52 am 
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B.

all laid it out it would be 1*(1-1/2)*1/2*1/2 which equals 1/8 which equals 2/16. should take 40 seconds MAX once you understand the reasoning


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  Re: M15 #31 [#permalink]
New postPosted: Sat Dec 10, 2011 11:26 pm 
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Yes B, got this one correct.


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  Re: M15 #31 [#permalink]
New postPosted: Sun Dec 11, 2011 3:48 pm 
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Read the question wrong initially so I did by the 4th throw. :(


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