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

It is currently 24 Aug 2016, 01:55
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 4 times. What is the probability of

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

Hide Tags

Intern
Intern
avatar
Joined: 04 Mar 2012
Posts: 46
Followers: 0

Kudos [?]: 173 [0], given: 10

A fair coin is tossed 4 times. What is the probability of [#permalink]

Show Tags

New post 30 Apr 2012, 01:05
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (01:00) correct 39% (00:50) wrong based on 282 sessions

HideShow timer Statistics

A fair coin is tossed 4 times. What is the probability of getting at least 2 tails?

A. 1/16
B. 1/2
C. 3/16
D. 11/16
E. 3/8
[Reveal] Spoiler: OA
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34393
Followers: 6247

Kudos [?]: 79333 [3] , given: 10016

Re: A fair coin is tossed 4 times. What is the probability of [#permalink]

Show Tags

New post 30 Apr 2012, 01:17
3
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
gmihir wrote:
A fair coin is tossed 4 times. What is the probability of getting at least 2 tails?

A. 1/16
B. 1/2
C. 3/16
D. 11/16
E. 3/8


Let's find the probability of the opposite event and subtract this value from 1.

The opposite event would be getting zero tails (so all heads) or 1 tail.

\(P(HHHH)=(\frac{1}{2})^4=\frac{1}{16}\).

\(P(THHH)=\frac{4!}{3!}*(\frac{1}{2})^4=\frac{4}{16}\), we are multiplying by \(\frac{4!}{3!}\) since THHH scenario can occur in number of ways: THHH, HTHH , HHTH, or HHHT (notice that \(\frac{4!}{3!}\) basically gives number of arrangements of 4 letters THHH out of which 3 H's are identcal).

\(P(T\geq{2})=1-(\frac{1}{16}+\frac{4}{16})=\frac{11}{16}\).

Answer: D.

Hope it's clear.
_________________

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

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34393
Followers: 6247

Kudos [?]: 79333 [0], given: 10016

Re: A fair coin is tossed 4 times. What is the probability of [#permalink]

Show Tags

New post 14 Jul 2013, 00:13
1 KUDOS received
Manager
Manager
avatar
Joined: 30 May 2013
Posts: 190
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Followers: 0

Kudos [?]: 52 [1] , given: 72

GMAT ToolKit User
Re: A fair coin is tossed 4 times. What is the probability of [#permalink]

Show Tags

New post 01 Sep 2013, 19:41
1
This post received
KUDOS
gmihir wrote:
A fair coin is tossed 4 times. What is the probability of getting at least 2 tails?

A. 1/16
B. 1/2
C. 3/16
D. 11/16
E. 3/8



Another method:

Let's find the probability of 2 tails , 3 tails and all 4 tails


P(TTTT)=((1/2)^4=1/16.

P(HTTT)=(4!/3!)*(1/2)^4=4/16, we are multiplying by 4C3 (notice that {4!/3!} basically gives number of arrangements of 4 letters HTTT out of which 3 T's are identcal).

P(TTHH) = 4C2*(1/2)^4 = 4!/2!*2!*(1/2)^4=6/16

Total Probablity = 1/16 + 4/16 + 6/16
=11/16
Manager
Manager
User avatar
Joined: 09 Jun 2013
Posts: 54
GMAT 1: 680 Q49 V33
GMAT 2: 690 Q49 V34
GPA: 3.86
WE: Analyst (Advertising and PR)
Followers: 1

Kudos [?]: 50 [0], given: 3

Re: A fair coin is tossed 4 times. What is the probability of [#permalink]

Show Tags

New post 01 Sep 2013, 23:31
1
This post was
BOOKMARKED
gmihir wrote:
A fair coin is tossed 4 times. What is the probability of getting at least 2 tails?

A. 1/16
B. 1/2
C. 3/16
D. 11/16
E. 3/8


Here's another approach that I used:

Total possibilities = 2^4= 16 since each toss leads to 2 outcomes.

Way of getting no tail in 4 tosses = 1 (H H H H)
Way of getting 1 tail in 4 tosses = 4 (T H H H) (H T H H) ( H H T H) (H H H T)
So ways of getting at least two tails in 4 tosses = 11 (16-5)
Therefore, the probability = 11/16 (D).
_________________

Don't be afraid to fail, but be afraid not to try

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11032
Followers: 509

Kudos [?]: 133 [0], given: 0

Premium Member
Re: A fair coin is tossed 4 times. What is the probability of [#permalink]

Show Tags

New post 23 Mar 2015, 11:47
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Intern
Intern
avatar
Joined: 13 Feb 2015
Posts: 7
Location: India
Concentration: General Management, Healthcare
WE: Research (Health Care)
Followers: 0

Kudos [?]: 9 [0], given: 24

The probability is 1/2 that a certain coin will turn heads on any give [#permalink]

Show Tags

New post 12 Aug 2015, 06:13
The probability is 1/2 that a certain coin will turn heads on any given toss. If a coin is to be tossed 4 times, what is the probability of getting at least 2 tails ?

1. 1/2
2. 1/16
3. 3/8
4. 5/8
5. 11/16
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34393
Followers: 6247

Kudos [?]: 79333 [0], given: 10016

Re: A fair coin is tossed 4 times. What is the probability of [#permalink]

Show Tags

New post 12 Aug 2015, 07:04
Manager
Manager
User avatar
Joined: 10 Jun 2015
Posts: 128
Followers: 1

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

Re: A fair coin is tossed 4 times. What is the probability of [#permalink]

Show Tags

New post 14 Aug 2015, 00:39
gmihir wrote:
A fair coin is tossed 4 times. What is the probability of getting at least 2 tails?

A. 1/16
B. 1/2
C. 3/16
D. 11/16
E. 3/8


Total outcome is 2^4=16
Number of cases of( tails < or =2) = 5, HHHH, THHH, HTHH, HHTH, HHHT
Therefore, the required probability is 11/16
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11032
Followers: 509

Kudos [?]: 133 [0], given: 0

Premium Member
Re: A fair coin is tossed 4 times. What is the probability of [#permalink]

Show Tags

New post 14 Aug 2016, 04:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: A fair coin is tossed 4 times. What is the probability of   [#permalink] 14 Aug 2016, 04:55
    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
Experts publish their posts in the topic A coin is tossed 4 times. What is the probability that the Splendidgirl666 4 18 Jan 2012, 03:32
48 Experts publish their posts in the topic A fair coin is tossed 5 times. What is the probability of nusmavrik 23 20 Aug 2010, 05:39
35 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
Display posts from previous: Sort by

A fair coin is tossed 4 times. What is the probability of

  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 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®.