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

It is currently 30 Apr 2016, 04:58
GMAT Club Tests

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 coin is tossed 5 times. What is the probability of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

3 KUDOS received
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: Chicago Booth Class of 2015
Joined: 26 Nov 2009
Posts: 994
Location: Singapore
Concentration: General Management, Finance
Schools: [color=#0000FF]Chicago Booth Class of 2015 [/color] - Class of 2015
WE: Information Technology (Retail Banking)
Followers: 19

Kudos [?]: 629 [3] , given: 36

A fair coin is tossed 5 times. What is the probability of [#permalink]

Show Tags

New post 20 Aug 2010, 05:39
3
This post received
KUDOS
19
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

48% (02:36) correct 52% (01:33) wrong based on 515 sessions

HideShow timer Statictics

A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?

A. 2/16
B. 1/4
C. 7/24
D. 5/16
E. 15/32
[Reveal] Spoiler: OA

_________________

Please press kudos if you like my post.

Expert Post
13 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5627

Kudos [?]: 68263 [13] , given: 9797

Re: Hard probability ! [#permalink]

Show Tags

New post 20 Aug 2010, 05:59
13
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
nusmavrik wrote:
A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?

A 2/16
B 1/4
C 7/24
D 5/16
E 15/32


At least 3 heads means 3, 4, or 5 heads.

3 consecutive heads
5 cases:
HHHTT
THHHT
TTHHH
HTHHH
HHHTH

\(P=5*(\frac{1}{2})^5=\frac{5}{32}\).

4 consecutive heads
2 cases:
HHHHT
THHHH

\(P=2*(\frac{1}{2})^5=\frac{2}{32}\).

5 consecutive heads
1 case:
HHHHH

\(P=(\frac{1}{2})^5=\frac{1}{32}\).

\(P=\frac{5}{32}+\frac{2}{32}+\frac{1}{32}=\frac{8}{32}=\frac{1}{4}\).

Answer: B.
_________________

New to the Math Forum?
Please read this: 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

Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: Chicago Booth Class of 2015
Joined: 26 Nov 2009
Posts: 994
Location: Singapore
Concentration: General Management, Finance
Schools: [color=#0000FF]Chicago Booth Class of 2015 [/color] - Class of 2015
WE: Information Technology (Retail Banking)
Followers: 19

Kudos [?]: 629 [0], given: 36

Re: Hard probability ! [#permalink]

Show Tags

New post 21 Aug 2010, 00:04
Awesome explanation Bunuel ! :-D
_________________

Please press kudos if you like my post.

1 KUDOS received
Manager
Manager
avatar
Joined: 27 May 2010
Posts: 203
Followers: 2

Kudos [?]: 34 [1] , given: 3

Re: Hard probability ! [#permalink]

Show Tags

New post 21 Aug 2010, 00:50
1
This post received
KUDOS
Brunnel explained it in detail. I would just count the number of possibilities and divide it by 2^n

HHHHH
HHHTT
HHHHT
THHHT
TTHHH
HHHTH
THHHH
HTHHH

8/(2)^5 ==> 8/32 ==> 1/4
Senior Manager
Senior Manager
avatar
Joined: 20 Apr 2010
Posts: 250
Location: Hyderabad
WE 1: 4.6 years Exp IT prof
Followers: 8

Kudos [?]: 36 [0], given: 49

Re: Hard probability ! [#permalink]

Show Tags

New post 21 Aug 2010, 13:54
All possible events = (1/2)^5= 1/32
all the favorable events
HHHHH
HHHTT
THHHT
TTHHH
HHHHT
THHHH
that makes 6 favourable events
Hence answer will 6/32 = 1/4 therefore B
_________________

I will give a Fight till the End

"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
- Bernard Edmonds

A person who is afraid of Failure can never succeed -- Amneet Padda

Don't Forget to give the KUDOS

Manager
Manager
avatar
Joined: 03 Aug 2011
Posts: 241
Location: United States
Concentration: General Management, Entrepreneurship
GMAT 1: 750 Q49 V44
GPA: 3.38
WE: Engineering (Computer Software)
Followers: 1

Kudos [?]: 40 [0], given: 12

Re: Hard probability ! [#permalink]

Show Tags

New post 23 Aug 2011, 17:11
my question is how do you determine from this problem, that immediately, you are going to have to map out the possibilities?

there seems to be no nifty way to do it other than really just exhausting the possibilities?

thanks
Senior Manager
Senior Manager
User avatar
Joined: 11 May 2011
Posts: 373
Location: US
Followers: 3

Kudos [?]: 82 [0], given: 46

Re: Hard probability ! [#permalink]

Show Tags

New post 23 Aug 2011, 17:51
Bunuel - U rock.
+1 for you.

Cheers.!
_________________

-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------

Manager
Manager
avatar
Joined: 26 Apr 2011
Posts: 230
Followers: 0

Kudos [?]: 10 [0], given: 12

GMAT ToolKit User CAT Tests
Re: Hard probability ! [#permalink]

Show Tags

New post 27 Dec 2011, 05:23
This is like another probability question asked in the forum, bunnel explained that very well.
Intern
Intern
avatar
Joined: 09 Mar 2012
Posts: 2
Followers: 0

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

PS: Probability [#permalink]

Show Tags

New post 24 Mar 2012, 11:53
A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?

A. 3/16
B. 1/4
C. 7/24
D. 5/16
E. 15/32

Kaplan says the answer is 1/4. I think the answer is 3/16 because I have interpreted the qn as: What is the probability of getting atleast 3 consecutive heads -> 3 consecutive heads or 4 consecutive heads or 5 consecutive heads ?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32549
Followers: 5627

Kudos [?]: 68263 [0], given: 9797

Re: PS: Probability [#permalink]

Show Tags

New post 24 Mar 2012, 14:29
Expert's post
shahlanuk wrote:
A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?

A. 3/16
B. 1/4
C. 7/24
D. 5/16
E. 15/32

Kaplan says the answer is 1/4. I think the answer is 3/16 because I have interpreted the qn as: What is the probability of getting atleast 3 consecutive heads -> 3 consecutive heads or 4 consecutive heads or 5 consecutive heads ?


Merging similar topics.

Your interpretation is correct: at least 3 consecutive heads means 3, 4, or 5 consecutive heads, but the answer is still 1/4. Please check the solution provided above and ask if anything remains unclear.
_________________

New to the Math Forum?
Please read this: 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

Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 647
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 43

Kudos [?]: 472 [0], given: 23

GMAT ToolKit User Premium Member Reviews Badge
Re: A fair coin is tossed 5 times. [#permalink]

Show Tags

New post 13 Nov 2012, 21:31
bellcurve wrote:
A fair coin is tossed 5 times, what is the probability of getting at least 3 heads on consecutive tosses?

-- Ans will be provided later.


Favorable outcomes:

HHHHH -- All heads

HHHHT -- 4 heads
THHHH

HHHTT -- 3 heads
THHHT
TTHHH
HTHHH
HHHTH



Total possiblities = 2^5 = 32
Favorable = 8
Probability = 8/32 = 1/4

Hope it helps!

PS: Please provide atleast options if not OA.
_________________

Lets Kudos!!! ;-)
Black Friday Debrief

Intern
Intern
avatar
Joined: 10 Nov 2012
Posts: 21
Concentration: Finance, International Business
GMAT Date: 01-16-2013
GPA: 3.37
WE: Management Consulting (Consulting)
Followers: 0

Kudos [?]: 1 [0], given: 6

Re: A fair coin is tossed 5 times. [#permalink]

Show Tags

New post 13 Nov 2012, 23:02
at least consecutive 3 heads
max consecutive 5 heads

5 heads - HHHHH (1 way)
4 heads - THHHH, HHHHT (2 ways)
3 heads - HHHTH, HHHTT, THHHT, HTHHH, TTHHH (5 ways)

Total 8 ways

Total no ways irrespective of outcome= 2x2x2x2x2 = 32

probability of atleast 3 consecutive heads = 8/32 or .25
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 17 Dec 2012
Posts: 427
Location: India
Followers: 22

Kudos [?]: 336 [1] , given: 12

Re: A fair coin is tossed 5 times. What is the probability of [#permalink]

Show Tags

New post 15 Jul 2013, 07:03
1
This post received
KUDOS
In this type of problems where repetition of values is allowed, the total number of possibilities is given by the formula \(n^r\) where n is 2 and has the values Heads and Tails. r is 5 and is equal to the number of tosses.

1. Total number of possibilities = \(2^5 = 32\)
2. Instances of favorable outcomes:

(i) HHH** - Let us elaborate all the possibilities:

1. HHH HH
2. HHH HT
3. HHH TH
4. HHH TT

We have exhausted the possibilities.

(ii) We also have the following **HHH and the possibilities are:

5. HH HHH
6.HT HHH
7,TH HHH
8.TT HHH

(iii) and the following: *HHH*

9. H HHH H
10, H HHH T
11. T HHH H
12. T HHH T

Out of the total 12 , only 8 are unique.

3. The probability is \(8/32 = 1/4.\)
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com

Classroom Courses in Chennai

Director
Director
avatar
Joined: 21 Dec 2009
Posts: 591
Concentration: Entrepreneurship, Finance
Followers: 17

Kudos [?]: 553 [0], given: 20

Re: A fair coin is tossed 5 times. What is the probability of [#permalink]

Show Tags

New post 16 Mar 2014, 09:30
I prefer using Binomial Expansion:

(H + T)^5: H^5 + 5H^4(T) + 10H^3*T^2 + 10H^2*T^3 + 5H*T^4 + T^5
The outcome for 3Heads 2 Tails = 10H^3*T^2 => 10*(1/32) = 5/16

The correct value should be 5/32

Can someone correct what am missing out here?

Thanks.
_________________

KUDOS me if you feel my contribution has helped you.

1 KUDOS received
Manager
Manager
User avatar
Joined: 24 Nov 2014
Posts: 71
GMAT 1: 800 Q51 V51
Followers: 9

Kudos [?]: 35 [1] , given: 6

Re: A fair coin is tossed 5 times. What is the probability of [#permalink]

Show Tags

New post 11 Jan 2015, 06:41
1
This post received
KUDOS
gmatbull wrote:
I prefer using Binomial Expansion:

(H + T)^5: H^5 + 5H^4(T) + 10H^3*T^2 + 10H^2*T^3 + 5H*T^4 + T^5
The outcome for 3Heads 2 Tails = 10H^3*T^2 => 10*(1/32) = 5/16

The correct value should be 5/32

Can someone correct what am missing out here?


Yes. It's not just three heads two tails. Its three heads in a row, AND, it could also be four heads in a row or five heads in a row.
_________________

Marty Murray
GMAT Coach
m.w.murray@hotmail.com
http://infinitemindprep.com

Senior Manager
Senior Manager
User avatar
Joined: 01 Nov 2013
Posts: 355
GMAT 1: 690 Q45 V39
WE: General Management (Energy and Utilities)
Followers: 4

Kudos [?]: 53 [0], given: 403

Reviews Badge CAT Tests
Re: A fair coin is tossed 5 times. What is the probability of [#permalink]

Show Tags

New post 09 Mar 2015, 06:06
I missed two cases
HHHTH and HTHHH .

Great solution by Bunnel.
_________________

Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.

I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.-Mohammad Ali

Intern
Intern
avatar
Joined: 10 May 2015
Posts: 30
Followers: 0

Kudos [?]: 1 [0], given: 268

GMAT ToolKit User
Re: A fair coin is tossed 5 times. What is the probability of [#permalink]

Show Tags

New post 23 May 2015, 00:57
Can someone suggest another way of solving this without writing down the possibilities? Maybe use combinations.An alternative could be useful in case you miss out on a case while jotting down the possibilities..thanks
Manager
Manager
User avatar
Joined: 13 Apr 2013
Posts: 94
Followers: 2

Kudos [?]: 48 [0], given: 540

Premium Member
A fair coin is tossed 5 times. What is the probability of [#permalink]

Show Tags

New post 20 Sep 2015, 21:56
Bunuel wrote:
nusmavrik wrote:
A fair coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses?

A 2/16
B 1/4
C 7/24
D 5/16
E 15/32


At least 3 heads means 3, 4, or 5 heads.

3 consecutive heads
5 cases:
HHHTT
THHHT
TTHHH
HTHHH
HHHTH

\(P=5*(\frac{1}{2})^5=\frac{5}{32}\).

4 consecutive heads
2 cases:
HHHHT
THHHH

\(P=2*(\frac{1}{2})^5=\frac{2}{32}\).

5 consecutive heads
1 case:
HHHHH

\(P=(\frac{1}{2})^5=\frac{1}{32}\).

\(P=\frac{5}{32}+\frac{2}{32}+\frac{1}{32}=\frac{8}{32}=\frac{1}{4}\).

Answer: B.


Hello Bunuel,

Can we solve this question by combination formula? Hope I am not asking wrong question. (Like for 3 consecutive heads= 5!/(3!*2!) x (1/2)^5. Using this, I am not getting 5/32. Please explain. Thanks
_________________

Freedom is not a gift...It is a responsibility to pass on.....

Expert Post
Jamboree GMAT Instructor
User avatar
Status: GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Joined: 15 Jul 2015
Posts: 294
Location: India
Followers: 51

Kudos [?]: 172 [0], given: 1

Re: A fair coin is tossed 5 times. What is the probability of [#permalink]

Show Tags

New post 25 Sep 2015, 21:31
Expert's post
In this question, i find "Counting" the cases is the best way to solve.

However, to answer the last question posted : In the combination (as is used by you for 3 consecutive heads) case, we are taking 3 heads in five tosses and not 3 consecutive heads in as many tosses.
_________________

Aryama Dutta Saikia
Jamboree Education Pvt. Ltd.
Jamboree Course Reviews | Try 2 of our classroom classes for free before you have to pay
Get GMAT Club Tests for free when you sign up for any Jamboree course. Request access

Re: A fair coin is tossed 5 times. What is the probability of   [#permalink] 25 Sep 2015, 21:31
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic Robert tossed a fair coin 3 times. What is the probability that the co Bunuel 4 27 Dec 2015, 09:04
19 Experts publish their posts in the topic A fair coin is tossed 6 times. What is the probability of getting no saikarthikreddy 12 23 Sep 2012, 03:34
16 Experts publish their posts in the topic A fair coin is tossed 4 times. What is the probability of gmihir 8 30 Apr 2012, 01:05
33 Experts publish their posts in the topic A fair coin is tossed 10 times. What is the probability that LM 28 22 Dec 2007, 21:57
8 A fair coin is tossed 5 times. What is the probability that netcaesar 10 24 May 2006, 23:30
Display posts from previous: Sort by

A fair coin is tossed 5 times. What is the probability of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.