Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 23 Aug 2016, 18:31

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# John throws a coin until a series of three consecutive heads

Author Message
SVP
Joined: 17 Jun 2008
Posts: 1570
Followers: 11

Kudos [?]: 233 [1] , given: 0

John throws a coin until a series of three consecutive heads [#permalink]

### Show Tags

20 Oct 2008, 05:17
1
KUDOS
4
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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
SVP
Joined: 07 Nov 2007
Posts: 1820
Location: New York
Followers: 30

Kudos [?]: 772 [6] , given: 5

### Show Tags

20 Oct 2008, 07:26
6
KUDOS
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

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
_________________

Smiling wins more friends than frowning

Senior Manager
Status: Happy to join ROSS!
Joined: 29 Sep 2010
Posts: 279
Concentration: General Management, Strategy
Schools: Ross '14 (M)
Followers: 19

Kudos [?]: 120 [2] , given: 48

### Show Tags

05 Dec 2010, 13:16
2
KUDOS
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
Manager
Joined: 23 Oct 2010
Posts: 87
Location: India
Followers: 3

Kudos [?]: 26 [1] , given: 6

### Show Tags

08 Dec 2010, 08:14
1
KUDOS
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
Intern
Joined: 03 Oct 2008
Posts: 17
Followers: 0

Kudos [?]: 1 [0], given: 0

### Show Tags

20 Oct 2008, 07:00
is d ans b....

1/16 + 1/16

2/16
SVP
Joined: 17 Jun 2008
Posts: 1570
Followers: 11

Kudos [?]: 233 [0], given: 0

### Show Tags

20 Oct 2008, 10:51
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

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.
Manager
Joined: 30 Apr 2009
Posts: 134
Followers: 1

Kudos [?]: 78 [0], given: 9

### Show Tags

22 Sep 2009, 08:26
nice explanation, got tricked by this Q.
_________________

Trying to make CR and RC my strong points

Intern
Joined: 24 Nov 2009
Posts: 27
Location: ny, ny
Followers: 0

Kudos [?]: 4 [0], given: 6

### Show Tags

30 Nov 2009, 14:33
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.
GMAT Forum Moderator
Status: Accepting donations for the mohater MBA debt repayment fund
Joined: 05 Feb 2008
Posts: 1866
Location: United States
Concentration: Operations, Finance
Schools: Ross '14 (M)
GMAT 1: 610 Q0 V0
GMAT 2: 710 Q48 V38
GPA: 3.54
WE: Accounting (Manufacturing)
Followers: 58

Kudos [?]: 729 [0], given: 234

### Show Tags

01 Dec 2009, 10:07

_________________

Strategy Discussion Thread | Strategy Master | GMAT Debrief| Please discuss strategies in discussion thread. Master thread will be updated accordingly. | GC Member Write Ups

GMAT Club Premium Membership - big benefits and savings

Intern
Joined: 29 Nov 2010
Posts: 5
Followers: 0

Kudos [?]: 1 [0], given: 2

### Show Tags

07 Dec 2010, 09:15
I said E.........DUMB MISTAKE!! I rushed it and forgot about the "consecutive" part.
Intern
Joined: 11 Nov 2010
Posts: 10
Followers: 0

Kudos [?]: 0 [0], given: 1

### Show Tags

07 Dec 2010, 15:34
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.
Manager
Joined: 08 Sep 2011
Posts: 75
Concentration: Finance, Strategy
Followers: 3

Kudos [?]: 2 [0], given: 5

### Show Tags

09 Dec 2011, 08:52
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
Manager
Joined: 20 Jan 2011
Posts: 65
Followers: 1

Kudos [?]: 1 [0], given: 8

### Show Tags

11 Dec 2011, 00:26
Yes B, got this one correct.
Manager
Joined: 21 Nov 2010
Posts: 133
Followers: 0

Kudos [?]: 5 [0], given: 12

### Show Tags

11 Dec 2011, 16:48
Read the question wrong initially so I did by the 4th throw.
Manager
Joined: 05 Sep 2012
Posts: 79
Followers: 2

Kudos [?]: 6 [0], given: 17

Re: John throws a coin until a series of three consecutive heads [#permalink]

### Show Tags

11 Dec 2012, 08:57
Got the Q and solution of this one.

Consecutive makes it a bit easy with only 2 desired cases.
Just wanted to understand the solution in case "consecutive" was not mentioned.

I think it will be an anagram in that case.

Favourable cases: ((For HHHT=: 4!/3!)+(For TTTH=:4!/3!))

Total cases= 4!

Can somebody confirm or point out mistakes in the modified Q (in case consecutive is not mentioned)??

Thanks

Last edited by soumens on 11 Dec 2012, 23:41, edited 1 time in total.
Current Student
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 152
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
Followers: 10

Kudos [?]: 268 [0], given: 35

Re: John throws a coin until a series of three consecutive heads [#permalink]

### Show Tags

11 Dec 2012, 20:58
very awesome question....got into the trap n selected 'D'...careful reading is so necessary....

Posted from my mobile device
_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Current Student
Joined: 11 Apr 2013
Posts: 53
Schools: Booth '17 (M)
Followers: 0

Kudos [?]: 27 [0], given: 13

Re: John throws a coin until a series of three consecutive heads [#permalink]

### Show Tags

05 Dec 2013, 12:35
My problem with this question is the way that it is worded. The phrase "What is the probability that the game ends after the fourth toss" could be interpreted as meaning what is the probabaility that the game does not end any time before the fifth throw, or in other words what is the probability that the game does not end on the fourth toss or before. This was my initial understanding, and although I eventually settled on what i assumed was the correct meaning (game ends right at fourth toss), I think this stem needs to be ammended to say "probability that the game ends immediately after the fourth throw" in order to be airtight.

Posted from my mobile device
Intern
Joined: 22 Jun 2011
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: John throws a coin until a series of three consecutive heads [#permalink]

### Show Tags

05 Dec 2013, 12:43
Using simple counting:

Possible outcomes (Green--> correct outcome, red --> false outcome): 0 represents tail, 1 represents head

0000
0001

0010
0011
0100
0101
0110
0111
1000

1001
1010
1011
1100
1101
1110
1111

probability = (correct outcome) / possible outcome

P = 2/16
Manager
Status: Work hard in silence, let success make the noise
Joined: 25 Nov 2013
Posts: 161
Location: India
Concentration: Finance, General Management
GMAT 1: 540 Q50 V15
GMAT 2: 640 Q50 V27
GPA: 3.11
WE: Consulting (Computer Software)
Followers: 7

Kudos [?]: 62 [0], given: 84

Re: John throws a coin until a series of three consecutive heads [#permalink]

### Show Tags

05 Dec 2013, 22:48
Excellent question...marked D on first attempt, but now understood why it is B.

1. THHH - 1/2 * 1/2 * 1/2 * 1/2 = 1/16
2. HTTT - 1/2 * 1/2 * 1/2 * 1/2 = 1/16

Adding both since it is either the first case or the second case.
So 1/16 + 1/16 = 2/16

So, B
_________________

Sahil Chaudhary
If you find this post helpful, please take a moment to click on the "+1 KUDOS" icon.
My IELTS 7.5 Experience
From 540 to 640...Done with GMAT!!!
http://www.sahilchaudhary007.blogspot.com

Intern
Joined: 14 Aug 2012
Posts: 20
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: John throws a coin until a series of three consecutive heads [#permalink]

### Show Tags

07 Dec 2013, 10:48
ans is B.
since the coin is tossed 4 times there can be 16 total outcomes.
there are only 2 outcomes that satisfy the condition.
HTTT and THHH.
Re: John throws a coin until a series of three consecutive heads   [#permalink] 07 Dec 2013, 10:48
Similar topics Replies Last post
Similar
Topics:
1 Mary and Joe are to throw three dice each 2 06 May 2012, 02:25
Binomial Series 1 02 Jan 2010, 07:52
Series - M3 - 29 3 13 Oct 2009, 21:18
gmatclub test question : mary and john 5 18 Mar 2009, 13:10
16 m04q36- Fish that had a 60 foot long head 22 09 Feb 2009, 16:23
Display posts from previous: Sort by

# John throws a coin until a series of three consecutive heads

Moderator: Bunuel

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.