M15 #31

scthakur · **Posted:** Mon Oct 20, 2008 4:17 am

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

AN225 · **Posted:** Sun Dec 05, 2010 12:16 pm

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

bindrakaran001 · **Posted:** Mon Oct 20, 2008 6:00 am

is d ans b....

1/16 + 1/16

2/16

x2suresh · **Posted:** Mon Oct 20, 2008 6:26 am

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

scthakur · **Posted:** Mon Oct 20, 2008 9:51 am

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.

kt00381n · **Posted:** Tue Sep 22, 2009 7:26 am

nice explanation, got tricked by this Q.

amittilak · **Posted:** Mon Nov 30, 2009 1:33 pm

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.

mohater · **Posted:** Tue Dec 01, 2009 9:07 am

Zanini · **Posted:** Tue Dec 07, 2010 8:15 am

I said E.........DUMB MISTAKE!! I rushed it and forgot about the "consecutive" part.

eladoren · **Posted:** Tue Dec 07, 2010 2:34 pm

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.

sleekmover · **Posted:** Wed Dec 08, 2010 7:14 am

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

Bowtie · **Posted:** Fri Dec 09, 2011 7:52 am

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

htskumar · **Posted:** Sat Dec 10, 2011 11:26 pm

Yes B, got this one correct.

Jdam · **Posted:** Sun Dec 11, 2011 3:48 pm

Read the question wrong initially so I did by the 4th throw.

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