Random Selection Paradox
$begingroup$
I was asked a question in an aptitude test, the statement of which is as follows:
"Out of 100 available equally likely choices we have to make 4 random selections. Goal is to have maximum randomness in the selection. Choices can be made in two ways:
You yourself make 4 random selections.
You select 4 random persons put of 100 so that they make 1 random selection out of 100.
Explain the reason behind your answer. Would it make any difference if we change the number of choices of available persons for selection."
This is how I approached toward the problem:
"When I randomly select 4 person out of hundred I would be making 4 choice out of 100 hundred available choice. These 4 choices would be determining my selection of 4 choices that is, event depended choice. In that case it can be possible that two or more persons out of 4 can make same choice thus decreasing randomness.
On the other hand,If I make choices and these choices are random then too repetition can be possible." This is where is am not able to do the reasoning. I seek you help in arriving at some conclusion. Thank you.
probability random
$endgroup$
|
show 1 more comment
$begingroup$
I was asked a question in an aptitude test, the statement of which is as follows:
"Out of 100 available equally likely choices we have to make 4 random selections. Goal is to have maximum randomness in the selection. Choices can be made in two ways:
You yourself make 4 random selections.
You select 4 random persons put of 100 so that they make 1 random selection out of 100.
Explain the reason behind your answer. Would it make any difference if we change the number of choices of available persons for selection."
This is how I approached toward the problem:
"When I randomly select 4 person out of hundred I would be making 4 choice out of 100 hundred available choice. These 4 choices would be determining my selection of 4 choices that is, event depended choice. In that case it can be possible that two or more persons out of 4 can make same choice thus decreasing randomness.
On the other hand,If I make choices and these choices are random then too repetition can be possible." This is where is am not able to do the reasoning. I seek you help in arriving at some conclusion. Thank you.
probability random
$endgroup$
$begingroup$
What does "maximum randomness" mean? I'd say you are aware of stochastic processes so you can use calculations and your knowledge to force the numbers to pass the whatever randomness determination test. Whereas if the numbers were actually chosen randomly they most likely won't score so highly.
$endgroup$
– fleablood
Dec 19 '18 at 6:20
$begingroup$
You are basically asking the following question: you have to generate $n$ random values. To get more “randomness”, is it better to have one or $n$ random number generators? I have never seen a computer code which heavily relies on new random nember generator for every new random value. In my opinion one good generator will be as good as many ones.
$endgroup$
– Oldboy
Dec 19 '18 at 6:44
$begingroup$
@fleablood I cannot say what 'maximum randomness' means because this is what was written in the question. Had there been any extra information, I could habe been more precise....... Are you saying that I can more precisely understand the problem if I do computer simulation of this? BTW thank you for your contribution.
$endgroup$
– R'am
Dec 19 '18 at 6:48
$begingroup$
@Oldboy yes I am asking what you said. ..... for what you argued can we mathematically analyse it or I have to do the computer simulation of it, for some 1000 runs, then plot it and establish statement for the same.
$endgroup$
– R'am
Dec 19 '18 at 6:52
$begingroup$
I was being snarky. What I was suggested would look random but would be the exact opposite in that it would be carefully calculated.
$endgroup$
– fleablood
Dec 19 '18 at 6:54
|
show 1 more comment
$begingroup$
I was asked a question in an aptitude test, the statement of which is as follows:
"Out of 100 available equally likely choices we have to make 4 random selections. Goal is to have maximum randomness in the selection. Choices can be made in two ways:
You yourself make 4 random selections.
You select 4 random persons put of 100 so that they make 1 random selection out of 100.
Explain the reason behind your answer. Would it make any difference if we change the number of choices of available persons for selection."
This is how I approached toward the problem:
"When I randomly select 4 person out of hundred I would be making 4 choice out of 100 hundred available choice. These 4 choices would be determining my selection of 4 choices that is, event depended choice. In that case it can be possible that two or more persons out of 4 can make same choice thus decreasing randomness.
On the other hand,If I make choices and these choices are random then too repetition can be possible." This is where is am not able to do the reasoning. I seek you help in arriving at some conclusion. Thank you.
probability random
$endgroup$
I was asked a question in an aptitude test, the statement of which is as follows:
"Out of 100 available equally likely choices we have to make 4 random selections. Goal is to have maximum randomness in the selection. Choices can be made in two ways:
You yourself make 4 random selections.
You select 4 random persons put of 100 so that they make 1 random selection out of 100.
Explain the reason behind your answer. Would it make any difference if we change the number of choices of available persons for selection."
This is how I approached toward the problem:
"When I randomly select 4 person out of hundred I would be making 4 choice out of 100 hundred available choice. These 4 choices would be determining my selection of 4 choices that is, event depended choice. In that case it can be possible that two or more persons out of 4 can make same choice thus decreasing randomness.
On the other hand,If I make choices and these choices are random then too repetition can be possible." This is where is am not able to do the reasoning. I seek you help in arriving at some conclusion. Thank you.
probability random
probability random
edited Dec 19 '18 at 6:05
R'am
asked Dec 19 '18 at 5:55
R'amR'am
11
11
$begingroup$
What does "maximum randomness" mean? I'd say you are aware of stochastic processes so you can use calculations and your knowledge to force the numbers to pass the whatever randomness determination test. Whereas if the numbers were actually chosen randomly they most likely won't score so highly.
$endgroup$
– fleablood
Dec 19 '18 at 6:20
$begingroup$
You are basically asking the following question: you have to generate $n$ random values. To get more “randomness”, is it better to have one or $n$ random number generators? I have never seen a computer code which heavily relies on new random nember generator for every new random value. In my opinion one good generator will be as good as many ones.
$endgroup$
– Oldboy
Dec 19 '18 at 6:44
$begingroup$
@fleablood I cannot say what 'maximum randomness' means because this is what was written in the question. Had there been any extra information, I could habe been more precise....... Are you saying that I can more precisely understand the problem if I do computer simulation of this? BTW thank you for your contribution.
$endgroup$
– R'am
Dec 19 '18 at 6:48
$begingroup$
@Oldboy yes I am asking what you said. ..... for what you argued can we mathematically analyse it or I have to do the computer simulation of it, for some 1000 runs, then plot it and establish statement for the same.
$endgroup$
– R'am
Dec 19 '18 at 6:52
$begingroup$
I was being snarky. What I was suggested would look random but would be the exact opposite in that it would be carefully calculated.
$endgroup$
– fleablood
Dec 19 '18 at 6:54
|
show 1 more comment
$begingroup$
What does "maximum randomness" mean? I'd say you are aware of stochastic processes so you can use calculations and your knowledge to force the numbers to pass the whatever randomness determination test. Whereas if the numbers were actually chosen randomly they most likely won't score so highly.
$endgroup$
– fleablood
Dec 19 '18 at 6:20
$begingroup$
You are basically asking the following question: you have to generate $n$ random values. To get more “randomness”, is it better to have one or $n$ random number generators? I have never seen a computer code which heavily relies on new random nember generator for every new random value. In my opinion one good generator will be as good as many ones.
$endgroup$
– Oldboy
Dec 19 '18 at 6:44
$begingroup$
@fleablood I cannot say what 'maximum randomness' means because this is what was written in the question. Had there been any extra information, I could habe been more precise....... Are you saying that I can more precisely understand the problem if I do computer simulation of this? BTW thank you for your contribution.
$endgroup$
– R'am
Dec 19 '18 at 6:48
$begingroup$
@Oldboy yes I am asking what you said. ..... for what you argued can we mathematically analyse it or I have to do the computer simulation of it, for some 1000 runs, then plot it and establish statement for the same.
$endgroup$
– R'am
Dec 19 '18 at 6:52
$begingroup$
I was being snarky. What I was suggested would look random but would be the exact opposite in that it would be carefully calculated.
$endgroup$
– fleablood
Dec 19 '18 at 6:54
$begingroup$
What does "maximum randomness" mean? I'd say you are aware of stochastic processes so you can use calculations and your knowledge to force the numbers to pass the whatever randomness determination test. Whereas if the numbers were actually chosen randomly they most likely won't score so highly.
$endgroup$
– fleablood
Dec 19 '18 at 6:20
$begingroup$
What does "maximum randomness" mean? I'd say you are aware of stochastic processes so you can use calculations and your knowledge to force the numbers to pass the whatever randomness determination test. Whereas if the numbers were actually chosen randomly they most likely won't score so highly.
$endgroup$
– fleablood
Dec 19 '18 at 6:20
$begingroup$
You are basically asking the following question: you have to generate $n$ random values. To get more “randomness”, is it better to have one or $n$ random number generators? I have never seen a computer code which heavily relies on new random nember generator for every new random value. In my opinion one good generator will be as good as many ones.
$endgroup$
– Oldboy
Dec 19 '18 at 6:44
$begingroup$
You are basically asking the following question: you have to generate $n$ random values. To get more “randomness”, is it better to have one or $n$ random number generators? I have never seen a computer code which heavily relies on new random nember generator for every new random value. In my opinion one good generator will be as good as many ones.
$endgroup$
– Oldboy
Dec 19 '18 at 6:44
$begingroup$
@fleablood I cannot say what 'maximum randomness' means because this is what was written in the question. Had there been any extra information, I could habe been more precise....... Are you saying that I can more precisely understand the problem if I do computer simulation of this? BTW thank you for your contribution.
$endgroup$
– R'am
Dec 19 '18 at 6:48
$begingroup$
@fleablood I cannot say what 'maximum randomness' means because this is what was written in the question. Had there been any extra information, I could habe been more precise....... Are you saying that I can more precisely understand the problem if I do computer simulation of this? BTW thank you for your contribution.
$endgroup$
– R'am
Dec 19 '18 at 6:48
$begingroup$
@Oldboy yes I am asking what you said. ..... for what you argued can we mathematically analyse it or I have to do the computer simulation of it, for some 1000 runs, then plot it and establish statement for the same.
$endgroup$
– R'am
Dec 19 '18 at 6:52
$begingroup$
@Oldboy yes I am asking what you said. ..... for what you argued can we mathematically analyse it or I have to do the computer simulation of it, for some 1000 runs, then plot it and establish statement for the same.
$endgroup$
– R'am
Dec 19 '18 at 6:52
$begingroup$
I was being snarky. What I was suggested would look random but would be the exact opposite in that it would be carefully calculated.
$endgroup$
– fleablood
Dec 19 '18 at 6:54
$begingroup$
I was being snarky. What I was suggested would look random but would be the exact opposite in that it would be carefully calculated.
$endgroup$
– fleablood
Dec 19 '18 at 6:54
|
show 1 more comment
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$begingroup$
What does "maximum randomness" mean? I'd say you are aware of stochastic processes so you can use calculations and your knowledge to force the numbers to pass the whatever randomness determination test. Whereas if the numbers were actually chosen randomly they most likely won't score so highly.
$endgroup$
– fleablood
Dec 19 '18 at 6:20
$begingroup$
You are basically asking the following question: you have to generate $n$ random values. To get more “randomness”, is it better to have one or $n$ random number generators? I have never seen a computer code which heavily relies on new random nember generator for every new random value. In my opinion one good generator will be as good as many ones.
$endgroup$
– Oldboy
Dec 19 '18 at 6:44
$begingroup$
@fleablood I cannot say what 'maximum randomness' means because this is what was written in the question. Had there been any extra information, I could habe been more precise....... Are you saying that I can more precisely understand the problem if I do computer simulation of this? BTW thank you for your contribution.
$endgroup$
– R'am
Dec 19 '18 at 6:48
$begingroup$
@Oldboy yes I am asking what you said. ..... for what you argued can we mathematically analyse it or I have to do the computer simulation of it, for some 1000 runs, then plot it and establish statement for the same.
$endgroup$
– R'am
Dec 19 '18 at 6:52
$begingroup$
I was being snarky. What I was suggested would look random but would be the exact opposite in that it would be carefully calculated.
$endgroup$
– fleablood
Dec 19 '18 at 6:54