GMAT Changed on April 16th - Read about the latest changes here

 It is currently 22 May 2018, 14:25

### 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 2 sided coin is flipped 6 times. What is the

Author Message
TAGS:

### Hide Tags

Intern
Joined: 29 Nov 2009
Posts: 20
Location: Toronto
A fair 2 sided coin is flipped 6 times. What is the [#permalink]

### Show Tags

Updated on: 28 Nov 2013, 06:51
3
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

62% (01:34) correct 38% (02:06) wrong based on 288 sessions

### HideShow timer Statistics

A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

A. 5/8
B. 3/4
C. 7/8
D. 57/64
E. 15/16

Hi all,
First post, I have to say is this site is an amazing resource. Thanks to everyone who contributes!

I understand how to get the denominator just fine, but I am missing something on the numerator. I read the answer, but something just isn't clicking.

Thanks!

Originally posted by brentbrent on 06 Dec 2009, 18:50.
Last edited by Bunuel on 28 Nov 2013, 06:51, edited 2 times in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 45251
Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

06 Dec 2009, 19:14
3
KUDOS
Expert's post
6
This post was
BOOKMARKED
brentbrent wrote:
Hi all,
First post, I have to say is this site is an amazing resource. Thanks to everyone who contributes!

Question:
A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

a) 5/8
b) 3/4
c) 7/8
d) 57/64
e) 15/16

I understand how to get the denominator just fine, but I am missing something on the numerator. I read the answer, but something just isn't clicking.

Thanks!

Welcome to Gmat Club forum.

It would be easier to calculate the probability of opposite event and subtract it from 1.
Opposite event: 0 tail, 1 tail, 6 tails.

Probability of getting no tails: $$\frac{1}{2^6}=\frac{1}{64}$$;

Probability of getting 1 tail: $$6C1*\frac{1}{2^6}=\frac{6}{64}$$, we must multiply by 6C1 or by 6 as tail can occur for any flip from 6, hence in 6 ways;

Probability of getting 6 tails: $$\frac{1}{2^6}=\frac{1}{64}$$

$$P=1-(\frac{1}{64}+\frac{6}{64}+\frac{1}{64})=\frac{56}{64}=\frac{7}{8}$$

For more on probability and combinatorics please refer to the link: GMAT MATH BOOK
_________________
VP
Joined: 05 Mar 2008
Posts: 1427
Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

06 Dec 2009, 20:14
2
KUDOS
1
This post was
BOOKMARKED
brentbrent wrote:
Hi all,
First post, I have to say is this site is an amazing resource. Thanks to everyone who contributes!

Question:
A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

a) 5/8
b) 3/4
c) 7/8
d) 57/64
e) 15/16

I understand how to get the denominator just fine, but I am missing something on the numerator. I read the answer, but something just isn't clicking.

Thanks!

the long way:
You have 4 options, tails twice, tails three times, tails 4 times, and tails 5 times

6!/2!4! = 15

tails three times
6!/3!3! = 20

tails four times
6!/4!2! = 15

tails 5 times
6!/5!1! = 6

sum all and you get 56
56/64 = 7/8
Intern
Joined: 29 Nov 2009
Posts: 20
Location: Toronto
Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

06 Dec 2009, 20:37
Bunnel and Iagomez, thanks for the timely responses!

Bunnel:
I was getting hung up on why 6C1 had to be multiplied by 6.

Thanks again to both of you.
Math Expert
Joined: 02 Sep 2009
Posts: 45251
Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

07 Dec 2009, 03:42
Expert's post
1
This post was
BOOKMARKED
brentbrent wrote:
Bunnel and Iagomez, thanks for the timely responses!

Bunnel:
I was getting hung up on why 6C1 had to be multiplied by 6.

Thanks again to both of you.

What I meant was, when counting probability of getting 1 tail when flipped 6 times, 1 tail can occur in 6 different ways:

THHHHH
HTHHHH
HHTHHH
HHHTHH
HHHHTH
HHHHHT

Generally probability of occurring event k times in n-time sequence could be expressed as:

$$P = C^n_k*p^k*(1-p)^{n-k}$$

In our case $$k=1$$ and $$n=6$$, so we get:

$$P = C^6_1*\frac{1}{2}*\frac{1}{2^5}=6*\frac{1}{2^6}=\frac{6}{64}$$

So $$\frac{1}{64}$$ should be multiplied by $$C^6_1$$, which is $$6$$.
_________________
Senior Manager
Joined: 23 Oct 2010
Posts: 364
Location: Azerbaijan
Concentration: Finance
Schools: HEC '15 (A)
GMAT 1: 690 Q47 V38
Re: A fair 2 sided coin is flipped 6 times. What is the [#permalink]

### Show Tags

11 Mar 2013, 13:50
1
KUDOS
"at least twice, but not more than 5 times" means exactly 2 times, 3 times, 4 times and 5 times

The probability of getting exactly k results out of n flips is nCk/2^n

6C2/2^6+6C3/2^6+6C4/2^6+6C5/2^6=(20+15+15+6)/2^6=56/64=(7*8)/(8*8)=7/8
_________________

Happy are those who dream dreams and are ready to pay the price to make them come true

I am still on all gmat forums. msg me if you want to ask me smth

Manager
Joined: 28 Apr 2013
Posts: 144
Location: India
GPA: 4
WE: Medicine and Health (Health Care)
Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

28 Nov 2013, 07:25
Bunuel wrote:
brentbrent wrote:
Bunnel and Iagomez, thanks for the timely responses!

Bunnel:
I was getting hung up on why 6C1 had to be multiplied by 6.

Thanks again to both of you.

What I meant was, when counting probability of getting 1 tail when flipped 6 times, 1 tail can occur in 6 different ways:

THHHHH
HTHHHH
HHTHHH
HHHTHH
HHHHTH
HHHHHT

Generally probability of occurring event k times in n-time sequence could be expressed as:

$$P = C^n_k*p^k*(1-p)^{n-k}$$

In our case $$k=1$$ and $$n=6$$, so we get:

$$P = C^6_1*\frac{1}{2}*\frac{1}{2^5}=6*\frac{1}{2^6}=\frac{6}{64}$$

So $$\frac{1}{64}$$ should be multiplied by $$C^6_1$$, which is $$6$$.

ok slight complicated; but will do it……………; let me know to find the basic formulas for the no. properties?

thanks
_________________

Thanks for Posting

LEARN TO ANALYSE

+1 kudos if you like

Manager
Joined: 20 Jan 2014
Posts: 165
Location: India
Concentration: Technology, Marketing
Re: A fair 2 sided coin is flipped 6 times. What is the [#permalink]

### Show Tags

21 Sep 2014, 21:05
Bunuel wrote:
brentbrent wrote:
Hi all,
First post, I have to say is this site is an amazing resource. Thanks to everyone who contributes!

Question:
A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

a) 5/8
b) 3/4
c) 7/8
d) 57/64
e) 15/16

I understand how to get the denominator just fine, but I am missing something on the numerator. I read the answer, but something just isn't clicking.

Thanks!

Welcome to Gmat Club forum.

It would be easier to calculate the probability of opposite event and subtract it from 1.
Opposite event: 0 tail, 1 tail, 6 tails.

Probability of getting no tails: $$\frac{1}{2^6}=\frac{1}{64}$$;

Probability of getting 1 tail: $$6C1*\frac{1}{2^6}=\frac{6}{64}$$, we must multiply by 6C1 or by 6 as tail can occur for any flip from 6, hence in 6 ways;

Probability of getting 6 tails: $$\frac{1}{2^6}=\frac{1}{64}$$

$$P=1-(\frac{1}{64}+\frac{6}{64}+\frac{1}{64})=\frac{56}{64}=\frac{7}{8}$$

For more on probability and combinatorics please refer to the link: GMAT MATH BOOK

Hi Bunuel,

I understand the numerator part.
2C6 + 3C6 + 4C6 + 5C6 = 56

but how to calculate denominator part. I mean how can i count total no of combinations. I am not getting 64 .
Like in normal cases if we calculate for 6 ball, we take 6! as total no of combinations.
_________________

Math Expert
Joined: 02 Sep 2009
Posts: 45251
Re: A fair 2 sided coin is flipped 6 times. What is the [#permalink]

### Show Tags

22 Sep 2014, 01:26
1
KUDOS
Expert's post
him1985 wrote:
Bunuel wrote:
brentbrent wrote:
Hi all,
First post, I have to say is this site is an amazing resource. Thanks to everyone who contributes!

Question:
A fair 2 sided coin is flipped 6 times. What is the probability that tails will be the result at least twice, but not more than 5 times?

a) 5/8
b) 3/4
c) 7/8
d) 57/64
e) 15/16

I understand how to get the denominator just fine, but I am missing something on the numerator. I read the answer, but something just isn't clicking.

Thanks!

Welcome to Gmat Club forum.

It would be easier to calculate the probability of opposite event and subtract it from 1.
Opposite event: 0 tail, 1 tail, 6 tails.

Probability of getting no tails: $$\frac{1}{2^6}=\frac{1}{64}$$;

Probability of getting 1 tail: $$6C1*\frac{1}{2^6}=\frac{6}{64}$$, we must multiply by 6C1 or by 6 as tail can occur for any flip from 6, hence in 6 ways;

Probability of getting 6 tails: $$\frac{1}{2^6}=\frac{1}{64}$$

$$P=1-(\frac{1}{64}+\frac{6}{64}+\frac{1}{64})=\frac{56}{64}=\frac{7}{8}$$

For more on probability and combinatorics please refer to the link: GMAT MATH BOOK

Hi Bunuel,

I understand the numerator part.
2C6 + 3C6 + 4C6 + 5C6 = 56

but how to calculate denominator part. I mean how can i count total no of combinations. I am not getting 64 .
Like in normal cases if we calculate for 6 ball, we take 6! as total no of combinations.

Each coin can land on heads or tails, so 2 ways. We have 6 coins, so total number of outcomes is 2*2*2*2*2*2 = 2^6.
_________________
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3454
Re: If a fair two-sided coin is flipped 6 times, what is the probability [#permalink]

### Show Tags

10 Sep 2016, 09:42
azamaka wrote:
If a fair two-sided coin is flipped 6 times, what is the probability that tails is the result at least twice but at most 5 times?

A) 5/8
B) 3/4
C) 7/8
D) 57/64
E) 15/16

Atleast twice but atmost 5 times could be written as 1 - P(No + Exactly once + All)

P(No time)=$$1/2^8$$
P(Exactly Once) = $$6/2^8$$
P(All) = $$1/2^8$$

So, Required P = 1- $$8/2^8$$ = 7/8. Hence, C
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub
Verbal Resources: All SC Resources at one place | All CR Resources at one place

Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11655
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: A fair 2 sided coin is flipped 6 times. What is the [#permalink]

### Show Tags

21 Feb 2018, 22:53
Hi All,

In probability questions, there are two results that you can calculate - what you WANT to have happen or what you DON'T want to have happen. Since there are so many different ways to flip 2, 3, 4 or 5 tails, it will be easier for us to calculate what we DON'T want (0, 1 or 6 tails).

Since each toss has 2 possible outcomes (heads or tails), there are 2^6 = 64 different results for 6 coin flips.

Of those 64 options...

0 tails -->
HHHHHH = 1 option

1 tail -->
THHHHH
HTHHHH
HHTHHH
HHHTHH
HHHHTH
HHHHHT = 6 options

6 tails -->
TTTTTT = 1 option

1 + 6 + 1 = 8 options (of the 64) that we DON'T want...

Thus 64/64 - 8/64 = 56/64 = 7/8 that we DO want.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: A fair 2 sided coin is flipped 6 times. What is the   [#permalink] 21 Feb 2018, 22:53
Display posts from previous: Sort by