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

It is currently 20 Oct 2014, 03:57

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A fair 2-sided coin is flipped 6 times. What is the

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 07 Dec 2009
Posts: 15
Followers: 0

Kudos [?]: 3 [0], given: 4

A fair 2-sided coin is flipped 6 times. What is the [#permalink] New post 16 Dec 2009, 09:01
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

51% (02:36) correct 49% (01:46) wrong based on 104 sessions
A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

(A) 5/8
(B) 3/4
(C) 7/8
(D) 57/64
(E) 15/16
[Reveal] Spoiler: OA

Last edited by Bunuel on 10 Feb 2012, 11:51, edited 1 time in total.
Edited the question and added the OA
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23331
Followers: 3599

Kudos [?]: 28591 [0], given: 2803

Re: Probability [#permalink] New post 16 Dec 2009, 09:16
Expert's post
2
This post was
BOOKMARKED
melissawlim wrote:
A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

(A) 5/8
(B) 3/4
(C) 7/8
(D) 57/64
(E) 15/16


It would be easier to calculate the probability of opposite event and subtract it from 1.
Opposite event: 0 tail, 1 tail, 6 tails.

Probability of getting no tails: \frac{1}{2^6}=\frac{1}{64};

Probability of getting 1 tail: 6C1*\frac{1}{2^6}=\frac{6}{64}, we must multiply by 6C1 or by 6 as tail can occur for any flip from 6, hence in 6 ways (*see more about this case below);

Probability of getting 6 tails: \frac{1}{2^6}=\frac{1}{64}

P=1-(\frac{1}{64}+\frac{6}{64}+\frac{1}{64})=\frac{56}{64}=\frac{7}{8}

Answer: C.


* Counting probability of getting 1 tail when flipped 6 times: 1 tail can occur in 6 different ways:

THHHHH
HTHHHH
HHTHHH
HHHTHH
HHHHTH
HHHHHT

Generally probability of occurring event k times in n-time sequence could be expressed as:

P = C^n_k*p^k*(1-p)^{n-k}

In our case k=1 and n=6, so we get:

P = C^6_1*\frac{1}{2}*\frac{1}{2^5}=6*\frac{1}{2^6}=\frac{6}{64}

So \frac{1}{64} should be multiplied by C^6_1, which is 6.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Manager
Manager
avatar
Joined: 09 May 2009
Posts: 204
Followers: 1

Kudos [?]: 89 [1] , given: 13

Re: Probability [#permalink] New post 16 Dec 2009, 09:23
1
This post received
KUDOS
lets find it out the other way
P of all head(or no tail)=1/2^6=1/64
P of all tail (or no head)=1/2^6=1/64
P of one tail=1/2^6 * 6 { multiply by 6 as there are 6 ways we can get one tail and each is having a probability of 1/2}
tot=1/64 + 1/64 + 6/64=1/8
reqd P=1-tot=1-1/8=7/8

C
_________________

GMAT is not a game for losers , and the moment u decide to appear for it u are no more a loser........ITS A BRAIN GAME

Manager
Manager
avatar
Joined: 25 Apr 2014
Posts: 152
Followers: 0

Kudos [?]: 23 [0], given: 1474

Re: A fair 2-sided coin is flipped 6 times. What is the [#permalink] New post 19 Jun 2014, 19:11
Hi Bunuel,

Shouldn't the value of K be equal to 2 as we are looking for atleast twice.And secondly can you please explain me how do we restrict here that tails do not occur for more than five times by using the formula.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23331
Followers: 3599

Kudos [?]: 28591 [1] , given: 2803

Re: A fair 2-sided coin is flipped 6 times. What is the [#permalink] New post 20 Jun 2014, 04:18
1
This post received
KUDOS
Expert's post
maggie27 wrote:
Hi Bunuel,

Shouldn't the value of K be equal to 2 as we are looking for atleast twice.And secondly can you please explain me how do we restrict here that tails do not occur for more than five times by using the formula.


The example there with formula is for getting 1 tail when flipped 6 times.

The solution uses P(good) = 1 - P(bad). So, P(2, 3, 4, or 5 tails) = 1 - P(0, 1, or 6 tails.)
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 25 Apr 2014
Posts: 152
Followers: 0

Kudos [?]: 23 [0], given: 1474

Re: A fair 2-sided coin is flipped 6 times. What is the [#permalink] New post 20 Jun 2014, 06:29
My bad :(
Thank You Bunuel :)
1 KUDOS received
Manager
Manager
avatar
Joined: 21 Sep 2012
Posts: 86
Location: United States
Concentration: Finance, Economics
Schools: CBS '17
GPA: 4
WE: General Management (Consumer Products)
Followers: 1

Kudos [?]: 33 [1] , given: 28

Re: A fair 2-sided coin is flipped 6 times. What is the [#permalink] New post 20 Jun 2014, 07:12
1
This post received
KUDOS
melissawlim wrote:
A fair 2-sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

(A) 5/8
(B) 3/4
(C) 7/8
(D) 57/64
(E) 15/16


Total possible outcomes when coined is tossed 6 time=2^6=4*4*4=64
Total possible outcomes getting 2 or 3 or 4 or 5 tails= 6C2+6C3+6C4+6C5=(6*5)/2+(6*5*4)/(3*2)+(6*5)/2+6=15+20+15+6=56
Probability of getting atleast 2 but not more than 5 times tails=56/64=7/8

Ans=C
Manager
Manager
User avatar
Joined: 23 Jan 2013
Posts: 147
Followers: 0

Kudos [?]: 12 [0], given: 22

Re: A fair 2-sided coin is flipped 6 times. What is the [#permalink] New post 20 Jun 2014, 22:35
Forgot considering 0 events))
Re: A fair 2-sided coin is flipped 6 times. What is the   [#permalink] 20 Jun 2014, 22:35
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Suppose you flip a fair coin six times. What is the probabi mikemcgarry 1 02 Jan 2013, 13:12
Experts publish their posts in the topic Susan flipped a fair coin N times. What fraction of the synecdoche 12 11 Jun 2012, 18:29
8 Experts publish their posts in the topic A fair 2 sided coin is flipped 6 times. What is the brentbrent 11 06 Dec 2009, 17:50
3 a fair 2-sided coin is flipped 6 times. what is the bmwhype2 3 18 May 2007, 20:56
Kaplan Problem Susan flipped a fair coin N times. what minhthel 1 11 Jul 2006, 08:45
Display posts from previous: Sort by

A fair 2-sided coin is flipped 6 times. What is the

  Question banks Downloads My Bookmarks Reviews Important topics  


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

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®.