Find all School-related info fast with the new School-Specific MBA Forum

It is currently 04 May 2015, 16:22

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Kate and Danny each have $10. Together, they flip a fair coin 5 times.

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
User avatar
Joined: 22 Jul 2009
Posts: 193
Followers: 4

Kudos [?]: 210 [0], given: 18

Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] New post 22 Sep 2009, 13:36
1
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (03:27) correct 37% (01:58) wrong based on 57 sessions
Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than $10 but less than $15?

(A) 5/16
(B) 1/2
(C) 12/30
(D) 15/32
(E) 3/8

Source: Manhattan GMAT Archive (tough problems set).doc
[Reveal] Spoiler: OA

_________________

Please kudos if my post helps.


Last edited by Bunuel on 17 Feb 2015, 11:34, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Manhattan GMAT Discount CodesKaplan GMAT Prep Discount CodesVeritas Prep GMAT Discount Codes
Manager
Manager
User avatar
Joined: 22 Jul 2009
Posts: 193
Followers: 4

Kudos [?]: 210 [0], given: 18

Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] New post 22 Sep 2009, 13:40
Decided to post this question as Manhattan's explanation was unnecessarily cumbersome.

Question asks for the probability of the coin landing tails up either 3 or 4 times = P(3t) + P(4t)

Binomial distribution formula: nCk p^k (1-p)^(n-k)

P(3t) = 5C3 (1/2)^3 (1/2)^2 = 10 (1/2)^5
P(4t) = 5C4 (1/2)^4 (1/2)^1 = 5 (1/2)^5

=> P(3t) + P(4t) = 15/32
_________________

Please kudos if my post helps.

3 KUDOS received
Senior Manager
Senior Manager
User avatar
Affiliations: SPG
Joined: 15 Nov 2006
Posts: 326
Followers: 11

Kudos [?]: 367 [3] , given: 20

Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] New post 01 Mar 2011, 04:28
3
This post received
KUDOS
Q: what is the probability of getting 3 or 4 heads if a fair coin is flipped 5 times.

total number of possibilities \(= 2 * 2 * 2 * 2 * 2 = 2^5\)

\(P(3) = \frac{5C3}{2^5} = \frac{10}{32}\)

\(P(4) = \frac{5C4}{2^5} = \frac{5}{32}\)

Required probability \(= P(3) + P(4) = \frac{15}{32}\)

_________________

press kudos, if you like the explanation, appreciate the effort or encourage people to respond.

Download the Ultimate SC Flashcards

Intern
Intern
avatar
Joined: 17 Oct 2011
Posts: 2
Concentration: Entrepreneurship, Marketing
GMAT Date: 11-25-2011
GPA: 3.9
Followers: 0

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

Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] New post 19 Oct 2011, 08:26
y arent we taking into account the probablility of 2 heads or 1
Manager
Manager
User avatar
Status: Next engagement on Nov-19-2011
Joined: 12 Jan 2011
Posts: 84
Location: New Delhi, India
Schools: IIM, ISB, & XLRI
WE 1: B.Tech (Information Technology)
Followers: 1

Kudos [?]: 10 [0], given: 5

Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] New post 19 Oct 2011, 10:20
deep5586 wrote:
y arent we taking into account the probablility of 2 heads or 1

For 2 & 1 heads Kate will end up with < $10 and we want her to win :-) . Therefore, only possibilities are 3 or 4 heads.

I made an educated guess and it worked fine. :-D

Ans- 'D'

MGMAT's anagram helped here as well.

HHHHT = 5!/4!*1! = 5
HHHTT = 5!/3!*2! = 10

Total acceptable cases = 15
Total cases = 32

P = 15/32 :-D
_________________

GMAT is an addiction and I am darn addicted

Preparation for final battel:
GMAT PREP-1 750 Q50 V41 - Oct 16 2011
GMAT PREP-2 710 Q50 V36 - Oct 22 2011 ==> Scored 50 in Quant second time in a row :-)
MGMAT---- -1 560 Q28 V39 - Oct 29 2011 ==> Left Quant half done and continued with Verbal. Happy to see Q39 :-)

My ongoing plan: http://gmatclub.com/forum/550-to-630-need-more-to-achieve-my-dream-121613.html#p989311

Appreciate by kudos !!

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 27215
Followers: 4228

Kudos [?]: 41011 [0], given: 5654

Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] New post 30 Oct 2014, 08:55
Expert's post
2
This post was
BOOKMARKED

Tough and Tricky questions: Probability.



Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than $10 but less than $15?

(A) 5/16
(B) 1/2
(C) 12/30
(D) 15/32
(E) 3/8
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

2 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 13 Jun 2013
Posts: 275
Followers: 7

Kudos [?]: 171 [2] , given: 12

Premium Member
Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] New post 31 Oct 2014, 01:56
2
This post received
KUDOS
Bunuel wrote:

Tough and Tricky questions: Probability.



Kate and Danny each have $10. Together, they flip a fair coin 5 times. Every time the coin lands on heads, Kate gives Danny $1. Every time the coin lands on tails, Danny gives Kate $1. After the five coin flips, what is the probability that Kate has more than $10 but less than $15?

(A) 5/16
(B) 1/2
(C) 12/30
(D) 15/32
(E) 3/8


total number of possible outcomes when coin will be flipped 5 times= 2^5=32

now, for kate to have more than $10, she must have min. 3 favorable and max. 4 favorable draws in the 5 throws. (because if she wins in all the 5 draws, then she will have $15)

kate will win, every time tails (T) appears on the coin.

case 1) kate wins in 3 draws and losses in two. so we have 3 T's and 2H's(T,T,T,H,H), which can arrange themselves in 5!/(3!)(2!)=10

case 2) kate wins in 4 draws and losses in the 1 draw. so we have 4 T's and 1H (T,T,T,T,H), which can arrange themselves in 5!/4!=5

thus total no. of favorable ways=10+5=15
and thus required probability=15/32
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 4767
Followers: 296

Kudos [?]: 52 [0], given: 0

Premium Member
Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times. [#permalink] New post 17 Feb 2015, 11:16
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Kate and Danny each have $10. Together, they flip a fair coin 5 times.   [#permalink] 17 Feb 2015, 11:16
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Kate and David each have $10. Together they flip a coin 5 bibha 6 13 Jul 2010, 08:43
Kate and Danny each have $10. Together, they flip a fair coin 5 times. powerka 0 17 Feb 2015, 11:16
8 KAte and David each have $10. Together they flip a coin 5 tarek99 2 05 Aug 2008, 10:34
Kate and David each have $10. Together they flip a coin 5 suntaurian 9 06 Mar 2008, 06:33
Kate and Danny each have $10. Together, they flip a fair briozeal 6 12 Feb 2007, 20:20
Display posts from previous: Sort by

Kate and Danny each have $10. Together, they flip a fair coin 5 times.

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.