A box contains four coins, of which two coins have heads on : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 14:23

### 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 box contains four coins, of which two coins have heads on

Author Message
TAGS:

### Hide Tags

Intern
Joined: 01 Dec 2012
Posts: 39
Location: India
WE: Project Management (Retail)
Followers: 1

Kudos [?]: 38 [4] , given: 10

A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

02 Mar 2013, 08:02
4
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

34% (02:26) correct 66% (01:22) wrong based on 148 sessions

### HideShow timer Statistics

A box contains four coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.

A. 2/5
B. 1/2
C. 4/5
D. 2/3
E. 3/4
[Reveal] Spoiler: OA
VP
Joined: 24 Jul 2011
Posts: 1126
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 124

Kudos [?]: 540 [1] , given: 19

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

02 Mar 2013, 18:24
1
KUDOS

How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)

Therefore probability = 4/5

Option C
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Manager
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 177
GMAT 1: 530 Q43 V20
GMAT 2: 560 Q42 V25
GMAT 3: 650 Q48 V31
Followers: 1

Kudos [?]: 62 [0], given: 65

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

02 Mar 2013, 19:33
I would say
There are total 4 coins of which only 2 coins have both heads, so the answer is 2/4 = 1/2.
Not sure whether each head can be treated separately...

Posted from my mobile device
_________________

KUDOS is a way to say Thank You

Intern
Joined: 01 Dec 2012
Posts: 39
Location: India
WE: Project Management (Retail)
Followers: 1

Kudos [?]: 38 [0], given: 10

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

02 Mar 2013, 23:20
GyanOne wrote:

How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)

Therefore probability = 4/5

Option C

Can you please explain this -
If I have already tossed the coin and have got a head then how is the probability of getting another head on the other face = 4/5 ??
Current Student
Joined: 28 Apr 2012
Posts: 311
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)
Followers: 28

Kudos [?]: 391 [0], given: 142

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

02 Mar 2013, 23:37
pariearth wrote:
A box contains four coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face(hidden face) of the coin tossed is also a head.
A. 2/5
B. 1/2
C. 4/5
D. 2/3
E. 3/4

Guys need a detailed explaination here..

If head comes out of toss, then the coin is among: two coins that have heads on both their faces and the normal one.

Total possible outcomes: 3 (HHT)
Possible head : 2 (ruling out the tail for the normal coin)

Probability = 2/3
_________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well."
― Voltaire

Press Kudos, if I have helped.
Thanks!

VP
Joined: 24 Jul 2011
Posts: 1126
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 124

Kudos [?]: 540 [7] , given: 19

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

03 Mar 2013, 04:27
7
KUDOS
Guys, the question says that a coin is picked at random and then tossed. This means that a coin is picked up from among the four available, and without determining what kind of coin it is, this coin is tossed. The outcome of this toss is heads.

@nt2010: The outcome of the toss (heads), can be obtained in five different ways, so you need to consider each head separately.

@pariearth: What we are trying to do is given that the toss yielded a head, find out if the coin is two-headed or not.

@ConnectTheDots: We are considering just one toss of the coin. The set of outcomes you have described does not come into the picture at all.

Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Manager
Status: Looking to improve
Joined: 15 Jan 2013
Posts: 177
GMAT 1: 530 Q43 V20
GMAT 2: 560 Q42 V25
GMAT 3: 650 Q48 V31
Followers: 1

Kudos [?]: 62 [0], given: 65

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

03 Mar 2013, 08:18
Thank you gyanOne.

What is the source of this question?
_________________

KUDOS is a way to say Thank You

Intern
Joined: 01 Dec 2012
Posts: 39
Location: India
WE: Project Management (Retail)
Followers: 1

Kudos [?]: 38 [0], given: 10

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

03 Mar 2013, 21:21
Nicely xplaind..+1 2u
GyanOne wrote:
Guys, the question says that a coin is picked at random and then tossed. This means that a coin is picked up from among the four available, and without determining what kind of coin it is, this coin is tossed. The outcome of this toss is heads.

@nt2010: The outcome of the toss (heads), can be obtained in five different ways, so you need to consider each head separately.

@pariearth: What we are trying to do is given that the toss yielded a head, find out if the coin is two-headed or not.

@ConnectTheDots: We are considering just one toss of the coin. The set of outcomes you have described does not come into the picture at all.

Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
Intern
Joined: 01 Dec 2012
Posts: 39
Location: India
WE: Project Management (Retail)
Followers: 1

Kudos [?]: 38 [0], given: 10

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

03 Mar 2013, 21:30
nt2010 wrote:
What is the source of this question?

This is from my not-so-famous tution class' study material.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7125
Location: Pune, India
Followers: 2134

Kudos [?]: 13653 [6] , given: 222

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

03 Mar 2013, 22:25
6
KUDOS
Expert's post
1
This post was
BOOKMARKED
pariearth wrote:
A box contains four coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face(hidden face) of the coin tossed is also a head.
A. 2/5
B. 1/2
C. 4/5
D. 2/3
E. 3/4

Guys need a detailed explaination here..

You can use the conditional probability concept here. You need to find the probability that the coin you tossed was a two-heads coin given that you got heads.

P(A given B) = P(A)/P(B)

P(A) = P(Two heads coins) = 2/4 = 1/2 (since 2 of the 4 coins have two heads)
P(B) = P(Getting heads on flipping a coin) = 5/8 (you have 5 heads and 3 tails in total on the 4 coins)

P(A given B) = (1/2)/(5/8) = 4/5

For more on conditional probability, check: http://www.veritasprep.com/blog/2012/02 ... onditions/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

VP
Joined: 24 Jul 2011
Posts: 1126
GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Followers: 124

Kudos [?]: 540 [0], given: 19

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

04 Mar 2013, 11:44
@pariearth.....you are certainly welcome. Do let us know if you face any further difficulty in understanding this concept. The important part of a probability problem is always setting it up by first understanding what is being asked.
_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93199 [2] , given: 10553

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

04 Mar 2013, 16:09
2
KUDOS
Expert's post
pariearth wrote:
A box contains four coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.

A. 2/5
B. 1/2
C. 4/5
D. 2/3
E. 3/4

More questions on conditional probability to practice:
if-ben-were-to-lose-the-championship-m07q12-75695.html
given-a-bag-with-2-black-balls-and-3-white-balls-126223.html

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13456
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

24 Apr 2014, 07:54
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 Legend
Joined: 09 Sep 2013
Posts: 13456
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: A box contains four coins, of which two coins have heads on [#permalink]

### Show Tags

05 Jul 2015, 09:59
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.
_________________
Re: A box contains four coins, of which two coins have heads on   [#permalink] 05 Jul 2015, 09:59
Similar topics Replies Last post
Similar
Topics:
4 What is the probability of tossing a coin five times and having heads 5 08 Dec 2014, 05:19
32 Matt is touring a nation in which coins are issued in two am 10 28 Jul 2014, 02:48
1 Coins are dropped into a toll box so that the box is being 3 05 Feb 2012, 16:15
7 Say you have 5 coins. 1 coin has heads on both sides and the 23 03 Nov 2009, 20:16
6 What is the probability of tossing a coin five times and having heads 14 17 Jun 2009, 05:10
Display posts from previous: Sort by