Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 May 2017, 16:25

### 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

# Marco and Maria toss a coin three times. Each time a head is

Author Message
TAGS:

### Hide Tags

VP
Joined: 22 Nov 2007
Posts: 1082
Followers: 8

Kudos [?]: 565 [1] , given: 0

Marco and Maria toss a coin three times. Each time a head is [#permalink]

### Show Tags

14 Jan 2008, 05:57
1
KUDOS
7
This post was
BOOKMARKED
00:00

Difficulty:

(N/A)

Question Stats:

74% (02:21) correct 26% (02:12) wrong based on 36 sessions

Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria $1. Each time a tail is obtained, Maria gives Marco$1. What is the probability that after the 3 tosses, Marco has $1 less than he did before the 3 tosses? it is an example with coins, without possible answer choices. please provide explanations. CEO Joined: 17 Nov 2007 Posts: 3586 Concentration: Entrepreneurship, Other Schools: Chicago (Booth) - Class of 2011 GMAT 1: 750 Q50 V40 Followers: 573 Kudos [?]: 3965 [1] , given: 360 Re: prob. example [#permalink] ### Show Tags 14 Jan 2008, 06:15 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED 3/8 Marco has$1 less than he did before the 3 tosses if we have 2 heads and 1 tail:
we use formula: p=nCm*p^m*q^(n-m)
where p - probability of a head
q - probability of a tail
m - the number of heads
n - the total number of tosses.

p=3C2*(1/2)^2*(1/2)=3/8
_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame

Director
Joined: 03 Sep 2006
Posts: 876
Followers: 7

Kudos [?]: 891 [3] , given: 33

### Show Tags

14 Jan 2008, 07:50
3
KUDOS
2
This post was
BOOKMARKED
marcodonzelli wrote:
Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria $1. Each time a tail is obtained, Maria gives Marco$1. What is the probability that after the 3 tosses, Marco has $1 less than he did before the 3 tosses? it is an example with coins, without possible answer choices. please provide explanations. Marco can have 1 dollar less than he had before the 3 tosses only in one case, i.e., when there is "H" twice and "T" once. THH = (1/2)^3 HTH = (1/2)^3 HHT = (1/2)^3 THH + HTH + HHT = 3/8 CEO Joined: 29 Mar 2007 Posts: 2562 Followers: 21 Kudos [?]: 453 [1] , given: 0 Re: prob. example [#permalink] ### Show Tags 15 Jan 2008, 11:01 1 This post received KUDOS marcodonzelli wrote: Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria$1. Each time a tail is obtained, Maria gives Marco $1. What is the probability that after the 3 tosses, Marco has$1 less than he did before the 3 tosses?

it is an example with coins, without possible answer choices. please provide explanations.

We need a WLL scencario. it will be 1/2*1/2*1/2 --> 1/8

Now WLL --> 3!/2!1! --> 3 - the number of possible arrangements of WLL. So 3*1/8 -> 3/8
SVP
Joined: 28 Dec 2005
Posts: 1562
Followers: 3

Kudos [?]: 158 [0], given: 2

### Show Tags

27 Jan 2008, 19:39
for him to end up with a buck less means that the outcome was two heads and one tail. And this can happen in any order.

So, using binomial theorem, we get: (3C2)*(1/2)^2*(1/2) = 3*1/8 = 3/8
SVP
Joined: 07 Nov 2007
Posts: 1809
Location: New York
Followers: 37

Kudos [?]: 930 [0], given: 5

### Show Tags

25 Aug 2008, 09:05
marcodonzelli wrote:
Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria $1. Each time a tail is obtained, Maria gives Marco$1. What is the probability that after the 3 tosses, Marco has $1 less than he did before the 3 tosses? it is an example with coins, without possible answer choices. please provide explanations. It should be two tails and 1 head. 3 WAYS possible = HTT+TTH+THT PROBABILITY = 3/ 2^3=3/8 _________________ Your attitude determines your altitude Smiling wins more friends than frowning Manager Joined: 27 Oct 2008 Posts: 185 Followers: 2 Kudos [?]: 150 [0], given: 3 Re: prob. example [#permalink] ### Show Tags 27 Sep 2009, 06:50 Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria$1. Each time a tail is obtained, Maria gives Marco $1. What is the probability that after the 3 tosses, Marco has$1 less than he did before the 3 tosses?

Soln: For Marco to lose one dollar, the possible events are (HHT,HTH,THH) = 3 ways
Total number of possibilites is = 2 * 2 * 2 = 8 ways

Thus probability that Marco loses 1$is = 3/8 Senior Manager Joined: 22 Dec 2009 Posts: 359 Followers: 11 Kudos [?]: 389 [0], given: 47 Re: prob. example [#permalink] ### Show Tags 14 Feb 2010, 15:18 marcodonzelli wrote: Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria$1. Each time a tail is obtained, Maria gives Marco $1. What is the probability that after the 3 tosses, Marco has$1 less than he did before the 3 tosses?

it is an example with coins, without possible answer choices. please provide explanations.

Can only happen.. if we have two Heads and one Tails....

HHT = (1/2)^3 x 3!/2! (Arrange HTT) = 3/8
_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Senior Manager
Joined: 01 Feb 2010
Posts: 264
Followers: 1

Kudos [?]: 57 [0], given: 2

### Show Tags

15 Feb 2010, 00:16
marcodonzelli wrote:
Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria $1. Each time a tail is obtained, Maria gives Marco$1. What is the probability that after the 3 tosses, Marco has $1 less than he did before the 3 tosses? it is an example with coins, without possible answer choices. please provide explanations. For Marco to have 1$ less than he did before the 3 tosses so 2 heads and one tail have to come.
p(event) = p(h)*p(h)*p(t) + p(h)*p(t)*p(h) + p(t)*p(h)*p(h) = (1/2)^3 + (1/2)^3 + (1/2)^3 = 3/8
Intern
Joined: 06 Jul 2011
Posts: 26
Followers: 1

Kudos [?]: 5 [0], given: 8

Re: Marco and Maria toss a coin three times. Each time a head is [#permalink]

### Show Tags

22 Jan 2012, 05:21
A combinatoric approach:

There are $$2^3$$ total permutations of possible results.

The ones where he ends up with -1$obviously consist of 2x head, 1x tails. We can calculate the number of ways this can happen (head, head, tails or head, tail, head etc.) with the formula $$\frac{P^3_3}{2!} = \frac{3!}{2!} = 3$$ ($$P^3_3$$ is the number of permutation of 3 different items. However, since 2 items are the same (head & head), we need to divide by the factorial of the number of equal items, so $$2!$$) This gives us a probabilitiy of $$\frac{\frac{P^3_3}{2!}}{2^3}=\frac{3}{8}$$ Math Expert Joined: 02 Sep 2009 Posts: 38798 Followers: 7714 Kudos [?]: 105766 [1] , given: 11581 Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 22 Jan 2012, 05:41 1 This post received KUDOS Expert's post 2 This post was BOOKMARKED marcodonzelli wrote: Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria$1. Each time a tail is obtained, Maria gives Marco $1. What is the probability that after the 3 tosses, Marco has$1 less than he did before the 3 tosses?

it is an example with coins, without possible answer choices. please provide explanations.

No need to complicate. The only way Marco to loose $1 is for HHT scenario --> Marco's balance=-1-1+1=-1. This scenario can occur in 3!/2! ways (# of permutations of 3 letters HHT out of which 2 H's are identical). As the total # of outcomes = 2^3 then P(HHT)=favorable/total=3/8. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15378 Followers: 648 Kudos [?]: 204 [0], given: 0 Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 08 Dec 2013, 10:37 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. _________________ Manager Joined: 28 Aug 2013 Posts: 99 Location: India Concentration: Operations, Marketing Schools: Insead '14, ISB '15 GMAT Date: 08-28-2014 GPA: 3.86 WE: Supply Chain Management (Manufacturing) Followers: 0 Kudos [?]: 39 [0], given: 23 Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 12 Sep 2014, 21:27 Its 3/8 Probability of individual event : 1/2 No. of individual events : 3 therefore 1/2 X 1/2 X 1/2 = 1/8 No. of ways in which we can contain favorable result : 3 they are HTT, THT, TTH thus 3X1/8 = 3/8 _________________ G-prep1 540 --> Kaplan 580-->Veritas 640-->MGMAT 590 -->MGMAT 2 640 --> MGMAT 3 640 ---> MGMAT 4 650 -->MGMAT 5 680 -- >GMAT prep 1 570 Give your best shot...rest leave upto Mahadev, he is the extractor of all negativity in the world !! Intern Joined: 14 Apr 2015 Posts: 6 Concentration: Human Resources, Technology GPA: 3.5 WE: Information Technology (Computer Software) Followers: 0 Kudos [?]: 0 [0], given: 75 Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 15 Jun 2015, 22:46 probability of wining=1/2 probability of loosing=1/2 So, 1/2*1/2*1/2*3c2=3/8 _________________ Regards, YS (I can,I WIL!!!) Intern Joined: 14 Apr 2015 Posts: 6 Concentration: Human Resources, Technology GPA: 3.5 WE: Information Technology (Computer Software) Followers: 0 Kudos [?]: 0 [0], given: 75 Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 15 Jun 2015, 22:51 bunnel i have one confusion its 3P2 or 3c2 _________________ Regards, YS (I can,I WIL!!!) GMAT Club Legend Joined: 09 Sep 2013 Posts: 15378 Followers: 648 Kudos [?]: 204 [0], given: 0 Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 29 Jun 2016, 21:27 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. _________________ Intern Joined: 26 Feb 2017 Posts: 9 Followers: 0 Kudos [?]: 2 [1] , given: 4 Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 16 Apr 2017, 21:13 1 This post received KUDOS Bunuel wrote: marcodonzelli wrote: Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria$1. Each time a tail is obtained, Maria gives Marco $1. What is the probability that after the 3 tosses, Marco has$1 less than he did before the 3 tosses?

it is an example with coins, without possible answer choices. please provide explanations.

No need to complicate. The only way Marco to loose $1 is for HHT scenario --> Marco's balance=-1-1+1=-1. This scenario can occur in 3!/2! ways (# of permutations of 3 letters HHT out of which 2 H's are identical). As the total # of outcomes = 2^8 then P(HHT)=favorable/total=3/8. Bunuel Should not be Total # of outcomes = 2^3 instead of 2^8 ?? Tks Math Expert Joined: 02 Sep 2009 Posts: 38798 Followers: 7714 Kudos [?]: 105766 [0], given: 11581 Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 16 Apr 2017, 23:49 vitorpteixeira wrote: Bunuel wrote: marcodonzelli wrote: Marco and Maria toss a coin three times. Each time a head is obtained, Marco gives Maria$1. Each time a tail is obtained, Maria gives Marco $1. What is the probability that after the 3 tosses, Marco has$1 less than he did before the 3 tosses?

it is an example with coins, without possible answer choices. please provide explanations.

No need to complicate. The only way Marco to loose \$1 is for HHT scenario --> Marco's balance=-1-1+1=-1. This scenario can occur in 3!/2! ways (# of permutations of 3 letters HHT out of which 2 H's are identical).

As the total # of outcomes = 2^8 then P(HHT)=favorable/total=3/8.

Bunuel

Should not be Total # of outcomes = 2^3 instead of 2^8 ??
Tks

Sure. It's 2^3 = 8 NOT 2^8 = 8. Edited. Thank you.
_________________
Re: Marco and Maria toss a coin three times. Each time a head is   [#permalink] 16 Apr 2017, 23:49
Similar topics Replies Last post
Similar
Topics:
Rick is three times as old as Maria, and Maria is four years older tha 2 10 Jan 2016, 08:53
4 What is the probability of tossing a coin five times and having heads 5 02 Mar 2015, 04:17
57 A fair coin is tossed 5 times. What is the probability of 24 21 May 2017, 01:30
6 What is the probability of tossing a coin five times and having heads 14 12 Nov 2015, 04:17
41 A fair coin is tossed 10 times. What is the probability that 28 10 Sep 2013, 21:07
Display posts from previous: Sort by