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How many times was a fair coin tossed? (1) If the coin has been tosse

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Bunuel
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How many times was a fair coin tossed? (1) If the coin has been tosse [#permalink] New post   27 May 2018, 10:19
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71% (01:20) correct 29% (01:28) wrong based on 434 sessions
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How many times was a fair coin tossed?

(1) If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8)
(2) When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.
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pushpitkc
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Re: How many times was a fair coin tossed? (1) If the coin has been tosse [#permalink] New post   28 May 2018, 05:48
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Bunuel wrote:
How many times was a fair coin tossed?

(1) If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8)
(2) When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.


1. When a fair coin is tossed once, the probability of getting heads on that toss is \(\frac{1}{2}\)
Similarly, when the fair coin is twice, the probability of getting heads on that toss is \(\frac{1}{2}*\frac{1}{2}\) = \(\frac{1}{4}\)
So, with every iteration of tossing the fair coin, we have an increase of \(\frac{1}{2}\)
If the coin was tossed 4 times fewer and the probability is \(\frac{1}{8}\)

If x is the number of times that the fair coin was tossed \(\frac{1}{2^{x-4}}\) = \(\frac{1}{2^3}\) -> \(x-4 = 3\) -> \(x = 7\) (Sufficient)


2. Every time a coin is tossed, there are 2 ouitcomes. So, if there are 128 outcomes possible,
and x is the number of times the coin is tossed, we have \(2^x = 128 = 2^7\) -> \(x = 7\) (Sufficient - Option D)
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Re: How many times was a fair coin tossed? (1) If the coin has been tosse [#permalink] New post   28 May 2018, 07:09
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Solution



To find:
    • How many times the fair coin is tossed

Analysing Statement 1
    • As per the information provided in Statement 1, the probability of getting heads on every toss would have been 1/8 if the coin has been tossed 4 times fewer
Now as we are tossing a fair coin, probability of getting a head if the coin is tossed
    • 1 time = \(\frac{1}{2}\)
    • 2 times = \((\frac{1}{2})^2\)
    • 3 times = \((\frac{1}{2})^3\)
    • Similarly, n times = \((\frac{1}{2})^n\)
Given that,
    • \((\frac{1}{2})^{n-4} = \frac{1}{8} = (\frac{1}{2})^3\)
    Hence, n – 4 = 3
    Or, n = 7
Hence, statement 1 is sufficient to answer

Analysing Statement 2
    • As per the information provided in Statement 2, when the coin is tossed the number of times, the number of different possible sequences of heads and tails is 128
Number of possible outcomes if the coin is tossed
    • 1 time = \(2^1\)
    • 2 times = \(2^2\)
    • 3 times = \(3^2\)
    • Similarly, n times = \(2^n\)
Given that,
    • \(2^n = 128 = 2^7\)
    Or, n = 7
Hence, statement 2 is sufficient to answer

Hence, the correct answer is option D.

Answer: D
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Re: How many times was a fair coin tossed? (1) If the coin has been tosse [#permalink] New post   23 Aug 2019, 09:09
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dabaobao wrote:
Bunuel wrote:
How many times was a fair coin tossed?

(1) If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8)
(2) When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.


VeritasKarishma Bunuel I have a doubt regarding this Q and really appreciate some help. Thanks!

I feel that the answer for this Q should be B since we can't assume the probability of getting a head to be 1/2. I know that we can't make any assumption on the GMAT DS section. Does GMAT always specify the probabilities for tossing a coin or rolling a dice or do we assume them when they are not given?

Statement 1 gives p^(n-4) = 1/2^3

I do realize that since n has to be an int, then I don't think p can be anything besides 2. I guess it's not a good quality question (not official anyway)?


How many times was a fair coin tossed?

A fair coin means that the probability of tails = the probability heads = 1/2.
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Re: How many times was a fair coin tossed? (1) If the coin has been tosse [#permalink] New post   23 Jun 2021, 06:25
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surabhimohan12 wrote:
How is probability of HHH different from HHT or HTT or TTT or THH or TTH or THH
Is it fair to say to probability of getting HHH is 1/8. Shouldn't we multiply this by 1/6


To your first question, yes, the probability here that you get the sequence HHH is identical to the probability that you get the sequence TTH or HTH, or any other specific sequence. Since there are 8 possible sequences:

HHH
HHT
HTH
THH
HTT
THT
TTH
TTT

and each sequence is equally likely, the probability we get one specific sequence like HHH is 1/8.

Naturally there are faster ways to do this, as the above solutions illustrate. I'm not sure exactly why you've asked about multiplying by 1/6, so I can't address that question.

I'd add, in case anyone is confused reading the question: the wording is wrong throughout (there are two separate grammar errors in Statement 1, and the first half of Statement 2 isn't in English). I suspect the question wasn't transcribed correctly.
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How many times was a fair coin tossed? (1) If the coin has been tosse [#permalink] New post   23 Aug 2019, 06:22
Bunuel wrote:
How many times was a fair coin tossed?

(1) If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8)
(2) When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.


VeritasKarishma Bunuel I have a doubt regarding this Q and really appreciate some help. Thanks!

I feel that the answer for this Q should be B since we can't assume the probability of getting a head to be 1/2. I know that we can't make any assumption on the GMAT DS section. Does GMAT always specify the probabilities for tossing a coin or rolling a dice or do we assume them when they are not given?

Statement 1 gives p^(n-4) = 1/2^3

I do realize that since n has to be an int, then I don't think p can be anything besides 2. I guess it's not a good quality question (not official anyway)?
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dabaobao
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Re: How many times was a fair coin tossed? (1) If the coin has been tosse [#permalink] New post   23 Aug 2019, 10:04
Bunuel wrote:
dabaobao wrote:
Bunuel wrote:
How many times was a fair coin tossed?

(1) If the coin has been tossed 4 times fewer, the probability of getting heads on every toss would have been (1/8)
(2) When a coin is tossed the number of times, the number of different possible sequences of heads and tails is 128.


VeritasKarishma Bunuel I have a doubt regarding this Q and really appreciate some help. Thanks!

I feel that the answer for this Q should be B since we can't assume the probability of getting a head to be 1/2. I know that we can't make any assumption on the GMAT DS section. Does GMAT always specify the probabilities for tossing a coin or rolling a dice or do we assume them when they are not given?

Statement 1 gives p^(n-4) = 1/2^3

I do realize that since n has to be an int, then I don't think p can be anything besides 2. I guess it's not a good quality question (not official anyway)?


How many times was a fair coin tossed?

A fair coin means that the probability of tails = the probability heads = 1/2.


Of course! I didn't notice the word "fair". Careless mistake :(

Thanks a lot!
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Re: How many times was a fair coin tossed? (1) If the coin has been tosse [#permalink] New post   23 Jun 2021, 06:17
How is probability of HHH different from HHT or HTT or TTT or THH or TTH or THH
Is it fair to say to probability of getting HHH is 1/8. Shouldn't we multiply this by 1/6
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Re: How many times was a fair coin tossed? [#permalink] New post   27 Dec 2022, 05:49
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Re: How many times was a fair coin tossed? [#permalink]
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