GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Feb 2019, 20:18

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
  • Free GMAT Algebra Webinar

     February 17, 2019

     February 17, 2019

     07:00 AM PST

     09:00 AM PST

    Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
  • Valentine's day SALE is on! 25% off.

     February 18, 2019

     February 18, 2019

     10:00 PM PST

     11:00 PM PST

    We don’t care what your relationship status this year - we love you just the way you are. AND we want you to crush the GMAT!

If an unbiased coin is flipped 5 times, the probability that

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

 
Manager
Manager
User avatar
Joined: 08 Sep 2010
Posts: 168
Location: India
WE 1: 6 Year, Telecom(GSM)
If an unbiased coin is flipped 5 times, the probability that  [#permalink]

Show Tags

New post Updated on: 28 Oct 2010, 02:43
8
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

31% (02:26) correct 69% (02:29) wrong based on 150 sessions

HideShow timer Statistics

If an unbiased coin is flipped 5 times, the probability that the same face does not show up in any three consecutive flips is

A. 1/2
B. 5/8
C. 3/8
D. 7/8
E. 9/8

_________________

Consider KUDOS if You find it good


Originally posted by ankitranjan on 28 Oct 2010, 01:41.
Last edited by ankitranjan on 28 Oct 2010, 02:43, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52906
Re: If an unbiased coin is flipped..... Help Needed  [#permalink]

Show Tags

New post 28 Oct 2010, 02:33
3
1
1
ankitranjan wrote:
If an unbiased coin is flipped 5 times,the probabilty that the same face does not show up in any three consecutive flips is

A. 1/2
B. 5/8
C. 3/8
D. 7/8
E. 9/8


Probably the easiest way would be just to write down the cases with at least 3 consecutive faces:

HHHHH
HHHHT
HHHTH
HHHTT

TTHHH
THHHH
HTHHH

THHHT

So we have 8 cases for at least 3 consecutive heads, which means that there will be also 8 cases for at least 3 consecutive tails. As there are total of 2^5 outcomes then the probability would be \(P=\frac{8+8}{2^5}=\frac{1}{2}\).

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
User avatar
Joined: 08 Sep 2010
Posts: 168
Location: India
WE 1: 6 Year, Telecom(GSM)
Re: If an unbiased coin is flipped..... Help Needed  [#permalink]

Show Tags

New post 28 Oct 2010, 02:45
Bunuel that was the right answer.Thanks for the explanation.
Senior Manager
Senior Manager
User avatar
Joined: 08 Nov 2010
Posts: 331
WE 1: Business Development
GMAT ToolKit User
Re: If an unbiased coin is flipped..... Help Needed  [#permalink]

Show Tags

New post 10 Nov 2010, 03:52
Bunuel, i know it will be the same answer, but shouldnt it be 1-p here?
_________________

GMAT Club Premium Membership - big benefits and savings

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 52906
Re: If an unbiased coin is flipped..... Help Needed  [#permalink]

Show Tags

New post 10 Nov 2010, 03:57
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 8882
Location: Pune, India
Re: If an unbiased coin is flipped..... Help Needed  [#permalink]

Show Tags

New post 10 Nov 2010, 06:48
ankitranjan wrote:
If an unbiased coin is flipped 5 times,the probabilty that the same face does not show up in any three consecutive flips is

A. 1/2
B. 5/8
C. 3/8
D. 7/8
E. 9/8


I agree with Bunuel. The easiest solution I could think of was enumerating in a sequence. I try and find how I can have the same face three or more times.

Start with 3 Hs and 2 Ts, go on to 4Hs and 1T and finally 5Hs
The 3 Hs have to be together so: HHHTT, TTHHH, THHHT
Then, 4 Hs and 1T. Place the 4 Hs first: H H H H. Now look for the places where you can place the T: THHHH, HTHHH, HHHTH and HHHHT
Finally 5 Hs: HHHHH
Total 8 ways to get 3 or more Heads in a row. Ways to get 3 or more Tails in a row is also 8.
Total number of ways outcomes with 5 coins = 2^5 = 32
Probability of same face occurring 3 or more times = 16/32 = 1/2
Probability of same face occurring less than 3 times = 1 - 1/2 = 1/2
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Intern
Intern
avatar
Joined: 17 Oct 2013
Posts: 40
Location: India
Concentration: Strategy, Statistics
Schools: ISB '17 (A)
GMAT 1: 730 Q49 V40
WE: Analyst (Computer Software)
Re: If an unbiased coin is flipped..... Help Needed  [#permalink]

Show Tags

New post 08 Nov 2013, 23:19
VeritasPrepKarishma wrote:
ankitranjan wrote:
If an unbiased coin is flipped 5 times,the probabilty that the same face does not show up in any three consecutive flips is

A. 1/2
B. 5/8
C. 3/8
D. 7/8
E. 9/8


I agree with Bunuel. The easiest solution I could think of was enumerating in a sequence. I try and find how I can have the same face three or more times.

Start with 3 Hs and 2 Ts, go on to 4Hs and 1T and finally 5Hs
The 3 Hs have to be together so: HHHTT, TTHHH, THHHT
Then, 4 Hs and 1T. Place the 4 Hs first: H H H H. Now look for the places where you can place the T: THHHH, HTHHH, HHHTH and HHHHT
Finally 5 Hs: HHHHH
Total 8 ways to get 3 or more Heads in a row. Ways to get 3 or more Tails in a row is also 8.
Total number of ways outcomes with 5 coins = 2^5 = 32
Probability of same face occurring 3 or more times = 16/32 = 1/2
Probability of same face occurring less than 3 times = 1 - 1/2 = 1/2



Is there a straighter way to solve this problem? Without going the opposite way
My attempt: Of the five slots, three straight slots are reserved for opposite results. (HTH, THT). The remaining two slots can yield a head or a tail.
So the possible number of outcomes is 2*2 = 4. Now these two slots are always clubbed together and can be treated as one slot that can be adjusted anywhere among the 4 possible slots in 4c1 ways. So the total possible outcomes under the given conditions will be 2*2* 4c1 = 16

Probability is 16/32 = 1/2

Is the thinking behind reaching this solution correct? Or did I just get lucky with the answer?

TIA
KC
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9839
Premium Member
Re: If an unbiased coin is flipped 5 times, the probability that  [#permalink]

Show Tags

New post 12 Oct 2018, 21:10
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: If an unbiased coin is flipped 5 times, the probability that   [#permalink] 12 Oct 2018, 21:10
Display posts from previous: Sort by

If an unbiased coin is flipped 5 times, the probability that

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.