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
Question Stats:
58% (02:07) correct 42% (02:33) wrong based on 332 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!
Official Answer and Stats are available only to registered users. Register/ Login.
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: 49496

Re: Combination problem  Princenten Review 2009 Bin 4 Q2
[#permalink]
Show Tags
06 Dec 2009, 19:14
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: \(\frac{1}{2^6}=\frac{1}{64}\) \(P=1(\frac{1}{64}+\frac{6}{64}+\frac{1}{64})=\frac{56}{64}=\frac{7}{8}\) Answer: C. Please ask if any question remains. For more on probability and combinatorics please refer to the link: GMAT MATH BOOK
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics




VP
Joined: 05 Mar 2008
Posts: 1421

Re: Combination problem  Princenten Review 2009 Bin 4 Q2
[#permalink]
Show Tags
06 Dec 2009, 20:14
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 let's start with tails twice( this means 2 tails 4 heads) 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: 49496

Re: Combination problem  Princenten Review 2009 Bin 4 Q2
[#permalink]
Show Tags
07 Dec 2009, 03:42



Senior Manager
Joined: 23 Oct 2010
Posts: 358
Location: Azerbaijan
Concentration: Finance

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



Manager
Joined: 28 Apr 2013
Posts: 136
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 ntime sequence could be expressed as: \(P = C^n_k*p^k*(1p)^{nk}\) 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: 156
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: \(\frac{1}{2^6}=\frac{1}{64}\) \(P=1(\frac{1}{64}+\frac{6}{64}+\frac{1}{64})=\frac{56}{64}=\frac{7}{8}\) Answer: C. Please ask if any question remains. For more on probability and combinatorics please refer to the link: GMAT MATH BOOKHi 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. Please help
_________________
Consider +1 Kudos Please



Math Expert
Joined: 02 Sep 2009
Posts: 49496

Re: A fair 2 sided coin is flipped 6 times. What is the
[#permalink]
Show Tags
22 Sep 2014, 01:26
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: \(\frac{1}{2^6}=\frac{1}{64}\) \(P=1(\frac{1}{64}+\frac{6}{64}+\frac{1}{64})=\frac{56}{64}=\frac{7}{8}\) Answer: C. Please ask if any question remains. For more on probability and combinatorics please refer to the link: GMAT MATH BOOKHi 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. Please help 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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? Extrahard Quant Tests with Brilliant Analytics



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3671

Re: If a fair twosided coin is flipped 6 times, what is the probability
[#permalink]
Show Tags
10 Sep 2016, 09:42
azamaka wrote: If a fair twosided 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  Importance of an Error Log! Verbal Resources: All SC Resources at one place  All CR Resources at one place Blog: Subscribe to Question of the Day Blog
GMAT Club Inbuilt Error Log Functionality  View More. New Visa Forum  Ask all your Visa Related Questions  here.
New! Best Reply Functionality on GMAT Club! Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12459
Location: United States (CA)

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. Final Answer: 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
CoFounder & 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!***********************



Senior Manager
Joined: 14 Dec 2017
Posts: 479

Re: A fair 2 sided coin is flipped 6 times. What is the
[#permalink]
Show Tags
15 Jun 2018, 01:38
brentbrent wrote: 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
Total # of Outcomes on flipping a coin for 6 times \(= 2^6 = 64\) Favorable outcomes = getting a tails at least twice but not more than 5 times Two Tails: TTHHHH = 6!/4!2! = 15 Three Tails: TTTHHH = 6!/3!3! = 20 Four Tails: TTTTHH = 6!/4!2! = 15 Five Tails: TTTTTH = 6!/5! = 6 Total # of favorable outcomes = 15 + 20 + 15 + 6 = 56 Required Probability = 56/64 = 7/8 Answer C. Thanks, GyM
_________________
New to GMAT Club  https://gmatclub.com/forum/newtogmatclubneedhelp271131.html#p2098335



Intern
Joined: 17 Jun 2018
Posts: 8

Re: A fair 2 sided coin is flipped 6 times. What is the
[#permalink]
Show Tags
19 Jun 2018, 06:13
Thank you so much for posting the question.




Re: A fair 2 sided coin is flipped 6 times. What is the &nbs
[#permalink]
19 Jun 2018, 06:13






