It is currently 20 Feb 2018, 11:32

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

Events & Promotions in June
Open Detailed Calendar

What is the probability of getting exactly three heads on

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

Hide Tags

3 KUDOS received
Retired Moderator
avatar
B
Joined: 17 Sep 2013
Posts: 386
Concentration: Strategy, General Management
GMAT 1: 730 Q51 V38
WE: Analyst (Consulting)
GMAT ToolKit User Premium Member Reviews Badge
What is the probability of getting exactly three heads on [#permalink]

Show Tags

New post 21 Apr 2014, 20:52
3
This post received
KUDOS
11
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

73% (00:56) correct 27% (01:08) wrong based on 398 sessions

HideShow timer Statistics

What is the probability of getting exactly three heads on five flips of a fair coin?

(A) 1/32
(B) 3/32
(C) 1/4
(D) 5/16
(E) 1/2

I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option
[Reveal] Spoiler: OA

_________________

Appreciate the efforts...KUDOS for all
Don't let an extra chromosome get you down..:P

3 KUDOS received
Manager
Manager
avatar
Joined: 12 May 2013
Posts: 79
Re: What is the probability of getting exactly three heads on [#permalink]

Show Tags

New post 21 Apr 2014, 22:59
3
This post received
KUDOS
3
This post was
BOOKMARKED
JusTLucK04 wrote:
What is the probability of getting exactly three heads on five flips of a fair coin?

(A) 1/32
(B) 3/32
(C) 1/4
(D) 5/16
(E) 1/2

I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option


i use this method, hope it helps
5!/3!*2!*1/2^5 = 5/16 (D)

5!/3!*2! = 5! as we flip the coin 5 times, divided by 3! as we want heads 3 times & 2! for tails

1/2^5 as probability of getting either a heads or a tails is 1/2 raise to 5 because we flip the coin 5 times

please give me kudos if it helps :)
Expert Post
3 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43831
Re: What is the probability of getting exactly three heads on [#permalink]

Show Tags

New post 22 Apr 2014, 00:38
3
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
JusTLucK04 wrote:
What is the probability of getting exactly three heads on five flips of a fair coin?

(A) 1/32
(B) 3/32
(C) 1/4
(D) 5/16
(E) 1/2

I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option


\(P(HHHTT)=\frac{5!}{3!2!}*(\frac{1}{2})^3*(\frac{1}{2})^2=\frac{10}{32}=\frac{5}{16}\), we need to multiply by \(\frac{5!}{3!2!}\) because HHHTT outcome can occur in several ways: HHHTTT, HHTHT, HTHHT, ..., TTHHH (\(\frac{5!}{3!2!}\) is permutation of 5 letters HHHTT).

Answer: D.
_________________

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
Status: Keep it simple stupid!!
Joined: 02 Mar 2016
Posts: 73
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q47 V36
GPA: 3.37
Re: What is the probability of getting exactly three heads on [#permalink]

Show Tags

New post 03 Sep 2016, 07:01
JusTLucK04 wrote:
What is the probability of getting exactly three heads on five flips of a fair coin?

(A) 1/32
(B) 3/32
(C) 1/4
(D) 5/16
(E) 1/2

I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option


5 Flips of a fair coin to get = HHHTT = no. of ways this can be achieved = 5!/3!x2! = 10

Probability to get any of the above 10 arrangements (HHHTT) = (1/2)^5 = 1/32

Total probability = 1/32 x 10 = 5/16
_________________

"Give without remembering, take without forgetting"
- Kudos

1 KUDOS received
Intern
Intern
avatar
B
Status: preparing
Joined: 30 Dec 2013
Posts: 41
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35
GMAT 2: 640 Q49 V28
GMAT 3: 640 Q49 V28
GMAT 4: 640 Q49 V28
GMAT 5: 640 Q49 V28
GPA: 2.84
WE: General Management (Consumer Products)
GMAT ToolKit User
Re: What is the probability of getting exactly three heads on [#permalink]

Show Tags

New post 20 Aug 2017, 03:37
1
This post received
KUDOS
Total number of ways to get 3 heads and 2 tails ( p(h) =p(t)= 1/2 for each)
=2^5=32

# of ways 3 heads can be arranged in 5 tosses= 5c3=10
10/32=5/16 ANS
SVP
SVP
avatar
P
Joined: 12 Dec 2016
Posts: 1906
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User Premium Member
Re: What is the probability of getting exactly three heads on [#permalink]

Show Tags

New post 25 Aug 2017, 17:14
2 ways:
1/ 5C2 / 2^5 => there are totally 2^5 different results, but only 5C2 favor results,
1/ (1/8) * (1/4) * 5C2
Intern
Intern
avatar
Joined: 19 Dec 2017
Posts: 8
Re: What is the probability of getting exactly three heads on [#permalink]

Show Tags

New post 30 Jan 2018, 23:36
HHHTT in any sequence would be required
Probability would be 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 5C3 = 1/32 x 10 = 5/16 (03 heads could be in any position, so 5C3)
Senior Manager
Senior Manager
avatar
S
Joined: 31 Jul 2017
Posts: 291
Location: Malaysia
WE: Consulting (Energy and Utilities)
Re: What is the probability of getting exactly three heads on [#permalink]

Show Tags

New post 08 Feb 2018, 01:39
JusTLucK04 wrote:
What is the probability of getting exactly three heads on five flips of a fair coin?

(A) 1/32
(B) 3/32
(C) 1/4
(D) 5/16
(E) 1/2

I am looking for a method better than counting...Consider if the Q had 10 coin flips or so..i.e counting would not be a feasible or practical option


No. of ways of selecting 3 Heads = \(5C3\)
Total number = \(32\)
\(P = \frac{5C3}{32}\)
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Re: What is the probability of getting exactly three heads on   [#permalink] 08 Feb 2018, 01:39
Display posts from previous: Sort by

What is the probability of getting exactly three heads on

  new topic post reply 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 | 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®.