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Randy is going to flip a coin x times. What is the minimum value of x

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pacifist85
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Randy is going to flip a coin x times. What is the minimum value of x [#permalink] New post   13 Mar 2015, 08:04
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Randy is going to flip a coin x times. What is the minimum value of x for which the probability that he flips all heads is less than 0.01%?

A. 10
B. 11
C. 12
D. 13
E. 14
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E
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Bunuel
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Re: Randy is going to flip a coin x times. What is the minimum value of x [#permalink] New post   13 Mar 2015, 08:21
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pacifist85 wrote:
Randy is going to flip a coin x times. What is the minimum value of x for which the probability that he flips all heads is less than 0.01%?

A 10

B 11

C 12

D 13

E 14


0.01% = 0.01/100 = 1/10,000;

(1/2)^x < 1/10,000;

2^x > 10,000;

\(x_{min}=14\) (2^10 = 1024, 2^13 = 1,024*2^3 < 10,000, so 2^14 must be greater than 10,000).

Answer: E.
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Re: Randy is going to flip a coin x times. What is the minimum value of x [#permalink] New post   13 Mar 2015, 08:07
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Hi, I am not sure if the difficulty level is correct. I did this one wrong, but see the official solution by veritas in the image:
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Re: Randy is going to flip a coin x times. What is the minimum value of x [#permalink] New post   13 Mar 2015, 08:13
I was wondering if it was necessary to go through this.

For example, we know that the probability of heads (or tails) is 1/2. To find how this probability changes according to the times we flip, we increase to the respective power. So, for 2 flips it would be (1/2)^2 = 1/4.

Now, to find the least number of flips that would produce a probability of less than 0.01%, couldn't we just plug in the higest number and see if it works?

So, we could do: (1/2)^14. We can relatively quickly find that 2^14= 16384. If we divide 1 by 16384 we end up with 0.000..., which is where we can stop the calculation, as it already is ower than 0.001.

Is this right?
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Randy is going to flip a coin x times. What is the minimum value of x [#permalink] New post   13 Mar 2015, 08:29
pacifist85 wrote:
Randy is going to flip a coin x times. What is the minimum value of x for which the probability that he flips all heads is less than 0.01%?

A. 10
B. 11
C. 12
D. 13
E. 14



\(P(H) = 1/2\)
if she flips X times, the probability of all HEADS is \((1/2)^x\)
question is asking
\(if (1/2)^x < 1/10000\) , what is the minimum value of x ?
\(x=14\)
Option E
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Re: Randy is going to flip a coin x times. What is the minimum value of x [#permalink] New post   13 Mar 2015, 22:38
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Hi pacifist85,

The question asks us to find the MINIMUM number of flips that will yield the desired result. By definition, the largest answer MUST be less than .01%, but we won't immediately know if that answer is the minimum answer.

The work that you would do to prove that 2^14 is less than .01% is essentially a 'step-by-step' calculation, so you should be able to tell if 2^12 or 2^13 was small enough (once you got to those 'steps' in the calculation). Since you're 'counting doubles' anyway, there's really not much of difference between what you're talking about and what the official solution provides.

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Re: Randy is going to flip a coin x times. What is the minimum value of x [#permalink] New post   04 Nov 2016, 07:49
pacifist85 wrote:
Randy is going to flip a coin x times. What is the minimum value of x for which the probability that he flips all heads is less than 0.01%?

A. 10
B. 11
C. 12
D. 13
E. 14


less than 0.01 = 1/100 * 1/100 = 1/10,000
(1/2)^2 = 1/4
^3 = 1/8
^4 = 1/16
^5 = 1/32
^6 = 1/64
^7 = 1/128
^8 = 1/256
^9 = 1/512
^10 = 1/1024 - A is out
^11 = 1/2048 - B is out
^12 = 1/4096 - C is out
^13 = 1/8192 - D is out

the answer must be E.

alternatively, we should know that 2^10 = 1024. - and we can start from there...
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Re: Randy is going to flip a coin x times. What is the minimum value of x [#permalink] New post   04 Nov 2016, 08:23
Here is a detailed solution.

Please don't hesitate if you have any question

Anis
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Re: Randy is going to flip a coin x times. What is the minimum value of x [#permalink] New post   27 Mar 2023, 06:14
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Re: Randy is going to flip a coin x times. What is the minimum value of x [#permalink]
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