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

 It is currently 05 May 2015, 02:34

### 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

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

Author Message
TAGS:
Director
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: 16

Kudos [?]: 481 [2] , given: 36

A fair coin is tossed 5 times. What is the probability of [#permalink]  20 Aug 2010, 04:39
2
KUDOS
8
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

46% (02:11) correct 54% (01:28) wrong based on 360 sessions
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.

Math Expert
Joined: 02 Sep 2009
Posts: 27227
Followers: 4229

Kudos [?]: 41042 [9] , given: 5660

Re: Hard probability ! [#permalink]  20 Aug 2010, 04:59
9
KUDOS
Expert's post
2
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

5 cases:
HHHTT
THHHT
TTHHH
HTHHH
HHHTH

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

2 cases:
HHHHT
THHHH

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

1 case:
HHHHH

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

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

_________________
Director
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: 16

Kudos [?]: 481 [0], given: 36

Re: Hard probability ! [#permalink]  20 Aug 2010, 23:04
Awesome explanation Bunuel !
_________________

Please press kudos if you like my post.

Manager
Joined: 27 May 2010
Posts: 203
Followers: 2

Kudos [?]: 27 [1] , given: 3

Re: Hard probability ! [#permalink]  20 Aug 2010, 23:50
1
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
Manager
Joined: 20 Apr 2010
Posts: 239
WE 1: 4.6 years Exp IT prof
Followers: 8

Kudos [?]: 54 [0], given: 47

Re: Hard probability ! [#permalink]  21 Aug 2010, 12:54
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
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 [?]: 39 [0], given: 12

Re: Hard probability ! [#permalink]  23 Aug 2011, 16:11
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
Joined: 11 May 2011
Posts: 374
Location: US
Followers: 3

Kudos [?]: 64 [0], given: 46

Re: Hard probability ! [#permalink]  23 Aug 2011, 16:51
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
Joined: 26 Apr 2011
Posts: 226
Followers: 0

Kudos [?]: 33 [0], given: 12

Re: Hard probability ! [#permalink]  27 Dec 2011, 04:23
This is like another probability question asked in the forum, bunnel explained that very well.
Senior Manager
Joined: 13 May 2011
Posts: 324
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 19

Kudos [?]: 154 [0], given: 11

Re: Hard probability ! [#permalink]  31 Dec 2011, 05:14
how common is "coin" probability question in real GMAT?
Intern
Joined: 09 Mar 2012
Posts: 2
Followers: 0

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

PS: Probability [#permalink]  24 Mar 2012, 10:53
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
Joined: 02 Sep 2009
Posts: 27227
Followers: 4229

Kudos [?]: 41042 [0], given: 5660

Re: PS: Probability [#permalink]  24 Mar 2012, 13:29
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.
_________________
Current Student
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 648
Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Followers: 38

Kudos [?]: 401 [0], given: 23

Re: A fair coin is tossed 5 times. [#permalink]  13 Nov 2012, 20:31
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:

THHHH

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
Joined: 10 Nov 2012
Posts: 21
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]  13 Nov 2012, 22:02

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
Math Expert
Joined: 02 Sep 2009
Posts: 27227
Followers: 4229

Kudos [?]: 41042 [0], given: 5660

Re: A fair coin is tossed 5 times. What is the probability of [#permalink]  13 Jul 2013, 23:08
Expert's post
Bumping for review and further discussion.
_________________
Senior Manager
Joined: 17 Dec 2012
Posts: 395
Location: India
Followers: 19

Kudos [?]: 243 [1] , given: 10

Re: A fair coin is tossed 5 times. What is the probability of [#permalink]  15 Jul 2013, 06:03
1
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 Test Prep
http://www.sravna.com

Classroom Courses in Chennai
Free Online Material

Director
Joined: 21 Dec 2009
Posts: 592
Concentration: Entrepreneurship, Finance
Followers: 16

Kudos [?]: 333 [0], given: 20

Re: A fair coin is tossed 5 times. What is the probability of [#permalink]  16 Mar 2014, 08:30
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.

Intern
Joined: 24 Nov 2014
Posts: 24
GMAT 1: 800 Q51 V51
Followers: 0

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

Re: A fair coin is tossed 5 times. What is the probability of [#permalink]  11 Jan 2015, 05:41
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

Manager
Joined: 01 Nov 2013
Posts: 114
WE: General Management (Energy and Utilities)
Followers: 0

Kudos [?]: 11 [0], given: 256

Re: A fair coin is tossed 5 times. What is the probability of [#permalink]  09 Mar 2015, 05:06
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

Re: A fair coin is tossed 5 times. What is the probability of   [#permalink] 09 Mar 2015, 05:06
Similar topics Replies Last post
Similar
Topics:
8 A fair coin is tossed 4 times. What is the probability of 5 30 Apr 2012, 00:05
29 A fair coin is tossed 10 times. What is the probability that 28 22 Dec 2007, 20:57
1 A fair coin is tossed 5 times. What is the probability 8 12 May 2007, 12:59
A fair coin is tossed 5 times.What is the probability that 4 13 Oct 2006, 13:23
7 A fair coin is tossed 5 times. What is the probability that 10 24 May 2006, 22:30
Display posts from previous: Sort by