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The probability that a biased coin falls heads is 1/4. What is the lea 02 Mar 2021, 03:00
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95% (hard)

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46% (02:19) correct 54% (02:15) wrong based on 143 sessions

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The probability that a biased coin falls heads is 1/4. What is the least number of times the coin must be thrown so that the probability of at least one head occurring is greater than 0.999?

A. 24
B. 25
C. 26
D. 27
E. 28

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The probability that a biased coin falls heads is 1/4. What is the lea 02 Mar 2021, 03:15
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1- Probability(No Head) > 0.999

Probability(No Head) < 0.001

Probability (Head) = 1/4

Probability (No Head) = 3/4

(3/4)^N < 0.001

N = 25

Hope this helps
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The probability that a biased coin falls heads is 1/4. What is the lea 07 Jul 2021, 13:32
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rvgmat12
1- Probability(No Head) > 0.999

Probability(No Head) < 0.001

Probability (Head) = 1/4

Probability (No Head) = 3/4

(3/4)^N < 0.001

N = 25

Hope this helps
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The equation is easy to get, but the question here is how you solve it without calculator.
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The probability that a biased coin falls heads is 1/4. What is the lea 19 Jul 2021, 13:58
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How do we get the value of n once we have the equation ready, without a calculator Bunuel
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The probability that a biased coin falls heads is 1/4. What is the lea 12 Dec 2021, 09:01
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rvgmat12
1- Probability(No Head) > 0.999

Probability(No Head) < 0.001

Probability (Head) = 1/4

Probability (No Head) = 3/4

(3/4)^N < 0.001

N = 25

Hope this helps
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How did you calculate this.
TIA
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The probability that a biased coin falls heads is 1/4. What is the lea 12 Dec 2021, 10:22
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rvgmat12
1- Probability(No Head) > 0.999

Probability(No Head) < 0.001

Probability (Head) = 1/4

Probability (No Head) = 3/4

(3/4)^N < 0.001

N = 25

Hope this helps
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How do we simplify (3/4)^N < 0.001 part?
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The probability that a biased coin falls heads is 1/4. What is the lea 12 Dec 2021, 10:57
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There's no chance at all you'd ever need to work with something like this on the GMAT, but we want the smallest value of n for which (3/4)^n < 1/1000. If you notice:

3^5 = 243
4^5 = 1024

you can see that 3^5/4^5 < 1/4. So raising both sides of this inequality to the fifth power,

(3^5/4^5)^5 < (1/4)^5
3^25/4^25 < 1/1024 < 1/1000

so that proves the answer here is at most 25, which gets us down to two answer choices. But (3/4)^24 is just negligibly greater than 1/1000 (here I'm using a calculator), so no similar estimation technique would ever let you rule out answer A, and I would be very surprised if there was any practical way using pen and paper to get the right answer here. You almost certainly need to do the calculation exactly, which isn't practical by hand. Not sure of the source, but this is not a GMAT question.
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The probability that a biased coin falls heads is 1/4. What is the lea 17 Dec 2021, 12:48
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IanStewart
There's no chance at all you'd ever need to work with something like this on the GMAT, but we want the smallest value of n for which (3/4)^n < 1/1000. If you notice:

3^5 = 243
4^5 = 1024

you can see that 3^5/4^5 < 1/4. So raising both sides of this inequality to the fifth power,

(3^5/4^5)^5 < (1/4)^5
3^25/4^25 < 1/1024 < 1/1000

so that proves the answer here is at most 25, which gets us down to two answer choices. But (3/4)^24 is just negligibly greater than 1/1000 (here I'm using a calculator), so no similar estimation technique would ever let you rule out answer A, and I would be very surprised if there was any practical way using pen and paper to get the right answer here. You almost certainly need to do the calculation exactly, which isn't practical by hand. Not sure of the source, but this is not a GMAT question.
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Approximately Log 2 = .30 log = 4 = .6 , log .475

-3 = N (.475 - .60)
-3 = N (-.125)

so N more close to 24 hence difficult
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The probability that a biased coin falls heads is 1/4. What is the lea 13 Nov 2025, 06:30
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Since the limits of approximation don't allow for discriminating between 24 and 25 this is a faulty question.

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