It is currently 21 Oct 2017, 00:11

### 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

Kudos [?]: 18 [2], given: 5

Location: Toronto
A fair 2 sided coin is flipped 6 times. What is the [#permalink]

### Show Tags

06 Dec 2009, 18:50
2
KUDOS
10
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:29) correct 42% (01:55) wrong based on 254 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!
[Reveal] Spoiler: OA

Last edited by Bunuel on 28 Nov 2013, 06:51, edited 2 times in total.
Edited the question and added the OA

Kudos [?]: 18 [2], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129061 [1], given: 12189

Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

06 Dec 2009, 19:14
1
KUDOS
Expert's post
4
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

[Reveal] Spoiler:
c

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
_________________

Kudos [?]: 129061 [1], given: 12189

VP
Joined: 05 Mar 2008
Posts: 1468

Kudos [?]: 300 [2], given: 31

Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

06 Dec 2009, 20:14
2
KUDOS
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

[Reveal] Spoiler:
c

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

Kudos [?]: 300 [2], given: 31

Intern
Joined: 29 Nov 2009
Posts: 20

Kudos [?]: 18 [0], given: 5

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.

Kudos [?]: 18 [0], given: 5

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129061 [0], given: 12189

Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

07 Dec 2009, 03:42
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 $$6$$.
_________________

Kudos [?]: 129061 [0], given: 12189

Senior Manager
Joined: 23 Oct 2010
Posts: 382

Kudos [?]: 395 [0], given: 73

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
"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

Kudos [?]: 395 [0], given: 73

Manager
Joined: 28 Apr 2013
Posts: 153

Kudos [?]: 75 [0], given: 84

Location: India
GPA: 4
WE: Medicine and Health (Health Care)
Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

27 Nov 2013, 19:56
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

[Reveal] Spoiler:
c

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

How do you calculate the prob of getting one tail in the any of the 6 flips as 6/64; can you let me know?

_________________

Thanks for Posting

LEARN TO ANALYSE

+1 kudos if you like

Kudos [?]: 75 [0], given: 84

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129061 [0], given: 12189

Re: Combination problem - Princenten Review 2009 Bin 4 Q2 [#permalink]

### Show Tags

28 Nov 2013, 06:52
rango 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

[Reveal] Spoiler:
c

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

How do you calculate the prob of getting one tail in the any of the 6 flips as 6/64; can you let me know?

Explained here: a-fair-2-sided-coin-is-flipped-6-times-what-is-the-87673.html#p659490

Hope it helps.
_________________

Kudos [?]: 129061 [0], given: 12189

Manager
Joined: 28 Apr 2013
Posts: 153

Kudos [?]: 75 [0], given: 84

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

Kudos [?]: 75 [0], given: 84

Current Student
Joined: 20 Jan 2014
Posts: 175

Kudos [?]: 69 [0], given: 120

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

[Reveal] Spoiler:
c

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.
_________________

Kudos [?]: 69 [0], given: 120

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 129061 [1], given: 12189

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

[Reveal] Spoiler:
c

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.
_________________

Kudos [?]: 129061 [1], given: 12189

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16610

Kudos [?]: 273 [0], given: 0

Re: A fair 2 sided coin is flipped 6 times. What is the [#permalink]

### Show Tags

11 Oct 2015, 21:32
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.
_________________

Kudos [?]: 273 [0], given: 0

BSchool Forum Moderator
Status: Aiming MBA
Joined: 18 Jul 2015
Posts: 2530

Kudos [?]: 798 [0], given: 64

Location: India
Concentration: Healthcare, Technology
GMAT 1: 710 Q50 V35
GPA: 3.65
WE: Information Technology (Health Care)
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
_________________

How I improved from V21 to V40! ?

Kudos [?]: 798 [0], given: 64

Re: If a fair two-sided coin is flipped 6 times, what is the probability   [#permalink] 10 Sep 2016, 09:42
Display posts from previous: Sort by