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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, 05:57
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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.
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.
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.
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
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
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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?
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
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
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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 $1 less than he did before the 3 tosses?
it is an example with coins, without possible answer choices. please provide explanations.
For Marco to have 1$ 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
Re: Marco and Maria toss a coin three times. Each time a head is [#permalink]
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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 \(\frac{\frac{P^3_3}{2!}}{2^3}=\frac{3}{8}\)
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.
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Re: Marco and Maria toss a coin three times. Each time a head is [#permalink]
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08 Dec 2013, 10:37
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Re: Marco and Maria toss a coin three times. Each time a head is [#permalink]
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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
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Re: Marco and Maria toss a coin three times. Each time a head is [#permalink]
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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).
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Re: Marco and Maria toss a coin three times. Each time a head is [#permalink]
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16 Apr 2017, 21:13
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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
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
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74% (02:21) correct
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