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

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Director
Joined: 22 Nov 2007
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Marco and Maria toss a coin three times. Each time a head is  [#permalink]

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14 Jan 2008, 04:57
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73% (01:18) correct 27% (02:06) wrong based on 69 sessions

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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. ##### Most Helpful Community Reply Director Joined: 03 Sep 2006 Posts: 573 Re: prob. example [#permalink] ### Show Tags 14 Jan 2008, 06:50 4 3 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
##### General Discussion
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14 Jan 2008, 05:15
1
1
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 Club Forum 2020 | GMAT ToolKit 2 (iOS) - The OFFICIAL GMAT CLUB PREP APPs, must-have apps especially if you aim at 700+ SVP Joined: 29 Mar 2007 Posts: 1648 Re: prob. example [#permalink] ### Show Tags 15 Jan 2008, 10:01 1 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
VP
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27 Jan 2008, 18:39
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
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25 Aug 2008, 08:05
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 Manager Joined: 27 Oct 2008 Posts: 125 Re: prob. example [#permalink] ### Show Tags 27 Sep 2009, 05:50 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 Manager Joined: 22 Dec 2009 Posts: 225 Re: prob. example [#permalink] ### Show Tags 14 Feb 2010, 14:18 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
Manager
Joined: 01 Feb 2010
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14 Feb 2010, 23:16
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
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Re: Marco and Maria toss a coin three times. Each time a head is  [#permalink]

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22 Jan 2012, 04:21
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: 65764 Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 22 Jan 2012, 04:41 1 2 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. _________________ Manager Joined: 28 Aug 2013 Posts: 73 Location: India Concentration: Operations, Marketing Schools: Insead '14, ISB '15 GMAT Date: 08-28-2014 GPA: 3.86 WE: Supply Chain Management (Manufacturing) Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 12 Sep 2014, 20:27 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: 5 Concentration: Human Resources, Technology GPA: 3.5 WE: Information Technology (Computer Software) Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 15 Jun 2015, 21:46 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: 26 Feb 2017 Posts: 28 Location: Brazil GMAT 1: 610 Q45 V28 GPA: 3.11 Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 16 Apr 2017, 20:13 1 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: 65764 Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 16 Apr 2017, 22:49 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. _________________ Current Student Joined: 30 Jan 2017 Posts: 7 Location: India Concentration: General Management, Marketing GMAT 1: 650 Q47 V35 GPA: 4 WE: Account Management (Advertising and PR) Re: Marco and Maria toss a coin three times. Each time a head is [#permalink] ### Show Tags 28 Jul 2017, 10:27 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 $1 is for HHT scenario --> Marco's balance=-1-1+1=-1. This scenario can occur in 3!/2! ways (# of permutations of 3 letters HHT out of which 2 H's are identical). As the total # of outcomes = 2^3 then P(HHT)=favorable/total=3/8. Would appreciate help with this! Does number of ways matter here? We are just concerned with the probability of Marco being -1$ and that's 1/8 right?
I'm not clear about why we need to consider the other variations of HHT when we are dealing with a money situation.

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

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29 Dec 2017, 07:38
Hi,

What is the approximate difficulty of this question on the 800 scale?

Thank you
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GMAT 1: 770 Q49 V46
Re: Marco and Maria toss a coin three times. Each time a head is  [#permalink]

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29 Dec 2017, 07:44
Top Contributor
krikre wrote:
Hi,

What is the approximate difficulty of this question on the 800 scale?

Thank you

I'd say around 600.

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

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10 Apr 2020, 19:52
Marco will be \$1 less when she has lost 2 chances and won 1 chances.
Possible cases for Marco
WLL + LWL + LLW
Every time Probability is 1/2×1/2×1/2 =1/8

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Re: Marco and Maria toss a coin three times. Each time a head is   [#permalink] 10 Apr 2020, 19:52