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

It is currently 24 Aug 2019, 10:54

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

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

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

Hide Tags

Find Similar Topics 
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 653
Location: Singapore
Concentration: General Management, Finance
Schools: Chicago Booth - Class of 2015
GMAT ToolKit User
A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post Updated on: 05 Feb 2019, 05:21
4
58
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (02:16) correct 55% (02:26) wrong based on 521 sessions

HideShow timer Statistics

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

Originally posted by nusmavrik on 20 Aug 2010, 05:39.
Last edited by Bunuel on 05 Feb 2019, 05:21, edited 1 time in total.
Renamed the topic.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57279
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post 20 Aug 2010, 05:59
26
11
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.
_________________
General Discussion
Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 26 Nov 2009
Posts: 653
Location: Singapore
Concentration: General Management, Finance
Schools: Chicago Booth - Class of 2015
GMAT ToolKit User
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post 21 Aug 2010, 00:04
Awesome explanation Bunuel ! :-D
Manager
Manager
avatar
Joined: 27 May 2010
Posts: 163
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post 21 Aug 2010, 00:50
2
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
Manager
Manager
avatar
S
Joined: 20 Apr 2010
Posts: 193
Location: Hyderabad
WE 1: 4.6 years Exp IT prof
Reviews Badge
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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: 211
Location: United States
Concentration: General Management, Entrepreneurship
GMAT 1: 750 Q49 V44
GPA: 3.38
WE: Engineering (Computer Software)
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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
B
Joined: 11 May 2011
Posts: 303
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post 23 Aug 2011, 17:51
1
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: 208
GMAT ToolKit User Reviews Badge
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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 ?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57279
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post 24 Mar 2012, 14:29
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.
_________________
Director
Director
User avatar
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 580
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
GMAT ToolKit User Reviews Badge
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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
B
Joined: 10 Nov 2012
Posts: 31
Location: United Arab Emirates
Concentration: Finance, International Business
Schools: INSEAD Jan '20
GMAT 1: 700 Q50 V34
GPA: 3.54
WE: Management Consulting (Commercial Banking)
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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
Director
Director
User avatar
S
Joined: 17 Dec 2012
Posts: 630
Location: India
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post 15 Jul 2013, 07:03
3
1
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 Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
Senior Manager
Senior Manager
avatar
Joined: 21 Dec 2009
Posts: 489
Concentration: Entrepreneurship, Finance
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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.
Target Test Prep Representative
User avatar
P
Status: Chief Curriculum and Content Architect
Affiliations: Target Test Prep
Joined: 24 Nov 2014
Posts: 570
GMAT 1: 800 Q51 V51
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post 11 Jan 2015, 06:41
1
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

Chief Curriculum and Content Architect

Marty@targettestprep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior Manager
Senior Manager
User avatar
B
Joined: 01 Nov 2013
Posts: 287
GMAT 1: 690 Q45 V39
WE: General Management (Energy and Utilities)
Reviews Badge
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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: 25
GMAT ToolKit User
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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
SVP
SVP
User avatar
V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1694
Location: India
Concentration: International Business, Operations
Schools: INSEAD Jan '19
GPA: 3.01
WE: Engineering (Real Estate)
Reviews Badge
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#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
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Jamboree GMAT Instructor
User avatar
Status: GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Joined: 15 Jul 2015
Posts: 272
Location: India
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post 25 Sep 2015, 21:31
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.
Intern
Intern
avatar
B
Joined: 19 Oct 2014
Posts: 36
Location: India
Concentration: Finance, Entrepreneurship
GMAT 1: 600 Q48 V25
GMAT 2: 670 Q49 V31
GPA: 3.26
WE: Operations (Manufacturing)
GMAT ToolKit User
Re: A fair coin is tossed 5 times. What is the probability of getting at  [#permalink]

Show Tags

New post 15 May 2016, 20:31
SravnaTestPrep wrote:
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 \(8/32 = 1/4.\)

How would you use this technique for atleast 2 heads ?
_________________
"Don't be satisfied with stories, how things have gone with others. Unfold your own myth."-Rumi

Consider hitting on kudos button for a sec, if this post helps you.
GMAT Club Bot
Re: A fair coin is tossed 5 times. What is the probability of getting at   [#permalink] 15 May 2016, 20:31

Go to page    1   2    Next  [ 28 posts ] 

Display posts from previous: Sort by

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

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





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