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# Susan flipped a fair coin N times. What fraction of the

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Intern
Joined: 28 May 2011
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Susan flipped a fair coin N times. What fraction of the [#permalink]

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11 Jun 2012, 19:29
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Susan flipped a fair coin N times. What fraction of the flips came up heads?

(1) N = 24
(2) The number of flips that came up tails was 3/8*N

Hi,

When you get a question like-

"X flipped a coin N times. What fraction of the flips came up heads?
(1) N=10
(2) 3/8N came up tails. "

Do you just answer B or do you try to be extra smart and ask whether it's a fair coin? (And hence, answer E)
[Reveal] Spoiler: OA

Last edited by Bunuel on 12 Jun 2012, 05:11, edited 1 time in total.
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11 Jun 2012, 19:57
Just answer B - I don't think GMAT would present such trick questions that need one to be 'extra smart' to get the correct answers.
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11 Jun 2012, 20:18
well, they do present some "trick" questions. for ex, in case of a DS question, involving a few variables like a<x<b, etc, everything would look easy except that it wouldn't have mentioned that x is an integer (i hope you get the example). so how is tht different from this? where do we draw the line?
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11 Jun 2012, 20:34
Hi,

Whenever you see a DS question you may expect the answer to be in form of a value or yes/no.

In the mentioned question, using (1), even if the coin is fair, we can only predict that probability of heads is 1/2 or 5 out of 10 turns.
but, the value (1/2) is practically based on large number of coin flips. It may happen that first 10 flips result in to 10 heads or no heads at all.

Thus, (1) is insufficient. (differentiating between the probability and actual results)

Using (2),
we get a straight forward answer:
so 5/8 of flips were heads.

Regards,
Intern
Joined: 28 May 2011
Posts: 29

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11 Jun 2012, 20:47
Hi,

Whenever you see a DS question you may expect the answer to be in form of a value or yes/no.

In the mentioned question, using (1), even if the coin is fair, we can only predict that probability of heads is 1/2 or 5 out of 10 turns.
but, the value (1/2) is practically based on large number of coin flips. It may happen that first 10 flips result in to 10 heads or no heads at all.

Thus, (1) is insufficient. (differentiating between the probability and actual results)

Using (2),
we get a straight forward answer:
so 5/8 of flips were heads.

Regards,

That doesn't exactly answer my question. I know how to solve it, however, the assumption is the coin is fair. If that's not given, then E should be the answer.
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11 Jun 2012, 20:50
Believe B is correct... we can safely assume here that coin is a Fair coin..
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11 Jun 2012, 21:25
Hi,

In GMAT, you don't need to take any assumption in DS question. In a particular info is required it would be mentioned.
Now in this question it doesn't matter whether the coin is unfair, since the choices don't require this assumption.

in (2), 3/8N are tails so other 5/8 should be heads.

Let me know if this is helpful.

Regards,
synecdoche wrote:
Hi,

Whenever you see a DS question you may expect the answer to be in form of a value or yes/no.

In the mentioned question, using (1), even if the coin is fair, we can only predict that probability of heads is 1/2 or 5 out of 10 turns.
but, the value (1/2) is practically based on large number of coin flips. It may happen that first 10 flips result in to 10 heads or no heads at all.

Thus, (1) is insufficient. (differentiating between the probability and actual results)

Using (2),
we get a straight forward answer:
so 5/8 of flips were heads.

Regards,

That doesn't exactly answer my question. I know how to solve it, however, the assumption is the coin is fair. If that's not given, then E should be the answer.
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GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38

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11 Jun 2012, 22:58
synecdoche wrote:
Hi,

When you get a question like-

"X flipped a coin N times. What fraction of the flips came up heads?
(1) N=10
(2) 3/8N came up tails. "

Do you just answer B or do you try to be extra smart and ask whether it's a fair coin? (And hence, answer E)

Were you asking wheter the coin has tails on both sides?

If so, then all flips would be tail, and statement (2) can't happen.

Regards,
Intern
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Posts: 31
Location: United States
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11 Jun 2012, 23:22
@ cyberjadugar - I think he means to ask if the coin has equal probability of Heads/Tails. A coin which is heavier on one side might not be fair.
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12 Jun 2012, 05:10
synecdoche wrote:
Hi,

When you get a question like-

"X flipped a coin N times. What fraction of the flips came up heads?
(1) N=10
(2) 3/8N came up tails. "

Do you just answer B or do you try to be extra smart and ask whether it's a fair coin? (And hence, answer E)

The GMAT will always make clear whether the coin is fair or not (for example it can be given that the probability of heads is 0.4 and the probability of tails is 0.6). So, you shouldn't worry about that issue.

Having said that, Kaplan also makes it clear in the original question, which is:
Susan flipped a fair coin N times. What fraction of the flips came up heads?
(1) N = 24
(2) The number of flips that came up tails was 3/8*N

Clearly, the first statement is not sufficient. Even though expected number of heads is 12 out of 24 but we don't know how many heads there were actually.

As for the second statement: since 3/8 of the flips came up tails then the remaining 5/8 of the flips must have been heads (provided N>0).

Hope it's clear.
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13 Jun 2012, 22:29
Bunuel wrote:
synecdoche wrote:
Hi,

When you get a question like-

"X flipped a coin N times. What fraction of the flips came up heads?
(1) N=10
(2) 3/8N came up tails. "

Do you just answer B or do you try to be extra smart and ask whether it's a fair coin? (And hence, answer E)

The GMAT will always make clear whether the coin is fair or not (for example it can be given that the probability of heads is 0.4 and the probability of tails is 0.6). So, you shouldn't worry about that issue.

Having said that, Kaplan also makes it clear in the original question, which is:
Susan flipped a fair coin N times. What fraction of the flips came up heads?
(1) N = 24
(2) The number of flips that came up tails was 3/8*N

Clearly, the first statement is not sufficient. Even though expected number of heads is 12 out of 24 but we don't know how many heads there were actually.

As for the second statement: since 3/8 of the flips came up tails then the remaining 5/8 of the flips must have been heads (provided N>0).

Hope it's clear.

Nice explanation Bunuel, if we assume that this is real GMAT question, and there is no indication that n>0 or it does not equal to 0, should we pick C as answer?
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14 Jun 2012, 00:45
ziko wrote:
Bunuel wrote:
synecdoche wrote:
Hi,

When you get a question like-

"X flipped a coin N times. What fraction of the flips came up heads?
(1) N=10
(2) 3/8N came up tails. "

Do you just answer B or do you try to be extra smart and ask whether it's a fair coin? (And hence, answer E)

The GMAT will always make clear whether the coin is fair or not (for example it can be given that the probability of heads is 0.4 and the probability of tails is 0.6). So, you shouldn't worry about that issue.

Having said that, Kaplan also makes it clear in the original question, which is:
Susan flipped a fair coin N times. What fraction of the flips came up heads?
(1) N = 24
(2) The number of flips that came up tails was 3/8*N

Clearly, the first statement is not sufficient. Even though expected number of heads is 12 out of 24 but we don't know how many heads there were actually.

As for the second statement: since 3/8 of the flips came up tails then the remaining 5/8 of the flips must have been heads (provided N>0).

Hope it's clear.

Nice explanation Bunuel, if we assume that this is real GMAT question, and there is no indication that n>0 or it does not equal to 0, should we pick C as answer?

Even though it's quite natural to assume that N must be more than zero, the real question would state it somehow to eliminate this ambiguity.
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Re: Susan flipped a fair coin N times. What fraction of the [#permalink]

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23 May 2013, 08:42
synecdoche wrote:
Susan flipped a fair coin N times. What fraction of the flips came up heads?

(1) N = 24
(2) The number of flips that came up tails was 3/8*N

Hi,

When you get a question like-

"X flipped a coin N times. What fraction of the flips came up heads?
(1) N=10
(2) 3/8N came up tails. "

Do you just answer B or do you try to be extra smart and ask whether it's a fair coin? (And hence, answer E)

u should have mentioned it as (3/8) *(8) this would have made the question much more clear.

for u ,

no we don't blindly keep B, when we know 3/8 so the rest are 2/8th thus we can find the ratio.
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Re: Susan flipped a fair coin N times. What fraction of the [#permalink]

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25 Jan 2016, 04:57
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Re: Susan flipped a fair coin N times. What fraction of the [#permalink]

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05 Aug 2016, 06:03
Suson flipped a fair coin N times. What fraction of the flips came up heads?

(1) N = 24
SO close yet so far. Because we know that the coin is a fair therefore the probability of getting heads is 50 % but probability does not mean "Definitely".

Since the question is asking "FRACTION" of HEAD which is $$\frac{# of HEAD}{# of TOTAL FLIPS}$$.

we cannot get this value because we dont know how many times the coin actually came as HEAD. All we know that its probability of gettting a head was 50% in each of the 24 tosses but how many times it was actually head is not known

INSUFFICIENT

(2) The number of flips that came up tails was 3/8*N

Number of times that tail came up = $$\frac{3N}{8}$$

Therefore total number of times head came up = $$\frac{5N}{8}$$

Fraction of head = $$\frac{5N}{8}*\frac{1}{N} =\frac{5}{8}$$of total

SUFFICIENT

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Re: Susan flipped a fair coin N times. What fraction of the   [#permalink] 05 Aug 2016, 06:03
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