NEW HERE? LEARN MORE
closeclose
Last visit was: 14 May 2024, 01:30 It is currently 14 May 2024, 01:30
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

A fair coin is flipped three times. What is the probability that the

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
BillyZ
Current Student
Joined: 14 Nov 2016
Posts: 1173
Own Kudos [?]: 20785 [27]
Given Kudos: 926
Location: Malaysia
Concentration: General Management, Strategy
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Send PM
GMAT ToolKit User Reviews Badge
A fair coin is flipped three times. What is the probability that the [#permalink] New post   21 Jan 2017, 18:57
2
Kudos
25
Bookmarks
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

74% (00:50) correct 26% (01:00) wrong based on 561 sessions
Hide Show timer Statistics
A fair coin is flipped three times. What is the probability that the coin lands on heads exactly twice?


A. \(\frac{1}{8}\)

B. \(\frac{3}{8}\)

C. \(\frac{1}{2}\)

D. \(\frac{5}{8}\)

E. \(\frac{7}{8}\)
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11248
Own Kudos [?]: 32497 [8]
Given Kudos: 301
Send PM
Reviews Badge Forum Quiz Mode
Re: A fair coin is flipped three times. What is the probability that the [#permalink] New post   21 Jan 2017, 20:38
3
Kudos
5
Bookmarks
Expert Reply
ziyuenlau wrote:
A fair coin is flipped three times. What is the probability that the coin lands on heads exactly twice?


A. \(\frac{1}{8}\)

B. \(\frac{3}{8}\)

C. \(\frac{1}{2}\)

D. \(\frac{5}{8}\)

E. \(\frac{7}{8}\)



Hi,

Ways of getting TWO heads in three flips..
3C2=3!/2!=3..

Total possible outcomes..
2*2*2=8..

Probability=3/8
B
User avatar
D
shashankism
Director
Director
Joined: 13 Mar 2017
Affiliations: IIT Dhanbad
Posts: 625
Own Kudos [?]: 593 [6]
Given Kudos: 88
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE:Engineering (Energy and Utilities)
Send PM
Re: A fair coin is flipped three times. What is the probability that the [#permalink] New post   13 Aug 2017, 13:42
5
Kudos
1
Bookmarks
hazelnut wrote:
A fair coin is flipped three times. What is the probability that the coin lands on heads exactly twice?


A. \(\frac{1}{8}\)

B. \(\frac{3}{8}\)

C. \(\frac{1}{2}\)

D. \(\frac{5}{8}\)

E. \(\frac{7}{8}\)


Probability of getting a head when a coin is flipped = 1/2
Probability of getting a tail when a coin is flipped = 1/2

Now coin is flipped thrice. The events in which coin lands in exactly 2 heads are THH, HTH, HHT

So required probability = 1/2*1/2*1/2 + 1/2*1/2*1/2 + 1/2*1/2*1/2 = 3/8

Answer B
General Discussion
User avatar
B
pra1785
Manager
Manager
Joined: 20 Jan 2016
Posts: 147
Own Kudos [?]: 128 [2]
Given Kudos: 64
Send PM
Re: A fair coin is flipped three times. What is the probability that the [#permalink] New post   13 Aug 2017, 13:29
2
Kudos
HHH
HHT
HTH
THH
TTT
TTH
THT
HTT

so there are 8 possible outcomes. 3 outcomes have only 2 heads. hence 3/8
avatar
anwesha1691
Intern
Intern
Joined: 09 Jun 2019
Posts: 3
Own Kudos [?]: 8 [2]
Given Kudos: 2
Send PM
Re: A fair coin is flipped three times. What is the probability that the [#permalink] New post   12 Jun 2019, 14:46
2
Kudos
We should remember the rule:
Probability (Complex Event) = Probability (Individual Event) * Arrangements

By that logic, we have to find the probability of heads appearing exactly twice i.e.,
P(HHT) - this becomes our complex event.

We can break this down to individual events such as,
P(H) * P(H) * P(T) which is 1/2 here for each case

Arrangement = 3!/2!
This is because the combination (HHT) can be arranged in 3 ways - (HHT), (HTH), (THH). Now we can’t always make cases if the sample space is huge so the formula for that is (total outcome)!/(repetitions)!

Thus,
Probability of heads appearing exactly twice = 1/2 * 1/2 * 1/2 * 3!/2! = 3/8

Answer: 3/8

Posted from my mobile device
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18850
Own Kudos [?]: 22208 [1]
Given Kudos: 285
Location: United States (CA)
Send PM
Re: A fair coin is flipped three times. What is the probability that the [#permalink] New post   17 Jun 2019, 17:43
1
Kudos
Expert Reply
hazelnut wrote:
A fair coin is flipped three times. What is the probability that the coin lands on heads exactly twice?


A. \(\frac{1}{8}\)

B. \(\frac{3}{8}\)

C. \(\frac{1}{2}\)

D. \(\frac{5}{8}\)

E. \(\frac{7}{8}\)


Let’s first considered the probability of H-H-T (i.e., two heads followed by a tail):

P(H-H-T) = (1/2)^3 = 1/8

However, two heads and one tail can occur in 3!/2! = 3 ways, so the total probability is 3 x 1/8 = 3/8.

Answer: B
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5975
Own Kudos [?]: 13470 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge Forum Quiz Mode
Re: A fair coin is flipped three times. What is the probability that the [#permalink] New post   21 Jul 2020, 08:30
1
Bookmarks
Expert Reply
BillyZ wrote:
A fair coin is flipped three times. What is the probability that the coin lands on heads exactly twice?


A. \(\frac{1}{8}\)

B. \(\frac{3}{8}\)

C. \(\frac{1}{2}\)

D. \(\frac{5}{8}\)

E. \(\frac{7}{8}\)


Method-1:

The number of ways of choosing 2 out of 3 heads\( = ^3C_2 = 3\)

Total outcomes of 3 tosses \(= 2*2*2 = 8\) (every toss has two outcomes H/T)

Required Probability \(= ^3C_2/2^3 = 3/8\)

Answer: Option B

Method-2:

Manually count outcomes of 3 tosses with two heads
(HHT), (HTH), (THH)

Total Outcomes = HHH, HHT, HTH, HTT, THH, THT, TTH, TTT = 8

Required Probability \(= 3/8\)

Answer: Option B

Subscribe to my YouTube Channel for FREE resource



Subscribe Topic-wise UN-bundled Video course. CHECK FREE Sample Videos
User avatar
D
minustark
Senior Manager
Senior Manager
Joined: 14 Jul 2019
Status:Student
Posts: 476
Own Kudos [?]: 370 [0]
Given Kudos: 52
Location: United States
Concentration: Accounting, Finance
Schools: Zicklin Baruch "22
GMAT 1: 650 Q45 V35
GPA: 3.9
WE:Education (Accounting)
Send PM
Reviews Badge
Re: A fair coin is flipped three times. What is the probability that the [#permalink] New post   25 Aug 2020, 13:04
BillyZ wrote:
A fair coin is flipped three times. What is the probability that the coin lands on heads exactly twice?



A. \(\frac{1}{8}\)

B. \(\frac{3}{8}\)

C. \(\frac{1}{2}\)

D. \(\frac{5}{8}\)

E. \(\frac{7}{8}\)


Exactly 2 heads can happen when HHT = 3!/2! = 3 ways to get this composition
Total ways = 2*2*2=8
Probability = 3/8
B is our answer.
User avatar
D
BrushMyQuant
Tutor
Joined: 05 Apr 2011
Status:Tutor - BrushMyQuant
Posts: 1778
Own Kudos [?]: 2100 [0]
Given Kudos: 100
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Send PM
Re: A fair coin is flipped three times. What is the probability that the [#permalink] New post   04 Oct 2022, 22:08
Expert Reply
Top Contributor
Given that A fair coin is flipped three times and we need to find What is the probability that the coin lands on heads exactly twice?

Coin is tossed 3 times => Total number of cases = \(2^3\) = 8

To find the cases in which the coin lands on heads exactly twice we need to select two places out of three _ _ _ in which we will get Heads.

This can be done in 3C2 ways = \(\frac{3!}{2!*(3-2)!}\) = \(\frac{3*2!}{2!*1!}\) = 3 ways

=> P(2H) = \(\frac{3}{8}\)

So, Answer will be B
Hope it helps!

Watch the following video to learn How to Solve Probability with Coin Toss Problems

User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32998
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: A fair coin is flipped three times. What is the probability that the [#permalink] New post   30 Nov 2023, 11:02
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 Club Bot
gmatclubot
Re: A fair coin is flipped three times. What is the probability that the [#permalink]
30 Nov 2023, 11:02
Moderators:
Bunuel
Math Expert
93248 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3136 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions