2
$\begingroup$

I want to draw a random number from 1 to 100. If this number is even, I want to then draw a random number from the odd numbers between 1 and 100. If the first number is odd, I want to draw a random number from the even numbers between 1 and 100.

Are the following three strategies the same?

(1) Draw a random number from the urn. Sort all odd (or even) numbers out and then draw a random number from the remaining numbers.

(2) Draw a random number from the urn. Draw a second number from the urn and put it back until the second number is not odd (or even).

(3) Draw two numbers from the urn and put them back until not both are odd (or even).

As a real world example, imagine I want to draw a proband from a pool of probands. I then want to pair this person off with a second proband of the opposite sex. I want the sex of the first proband to be random (e.g. because of sequence effects), therefore I cannot draw first a man and then a woman, or vice versa. I could draw first a man before a woman, then a woman before a man, then again a man before a woman etc. But I want to avoid the predictable regularity of that.

Contrary to the notification that pops up when I enter the title for this question, this is not a subjective question asking for opinions or guesses. I am sure the "relative randomness" of the events can be calculated: I would guess that you'd have to calculate the probabilities to draw a specific number under all three conditions, and the best "relative randomness" will be achieved, where this number has the lowest probability. Unfortunately, I don't know how to calculate this. Therefore I ask here.

I did not know the proper tags for this question. Please change them, if you feel others fit better.

$\endgroup$
4
  • 2
    $\begingroup$ Why not draw a man from the men and then a woman from the women, and then randomly hand one of them the label 'first'? What sequence effects are you anticipating, exactly? $\endgroup$
    – Glen_b
    Apr 6, 2013 at 5:48
  • $\begingroup$ Imagine the man and the woman will have to interact with a third person (the experimenter) in the order they were drawn. If the man is always first, that might influence the experimenter's behavior toward the woman (as always second), for example the experimenter could always be more tired with the second person, or judge the female behavior different if "primed" by male behavior (there are many situations where behavior is "measured" through judgements by trained observers). etc. $\endgroup$
    – user14650
    Apr 6, 2013 at 11:11
  • $\begingroup$ Why would they have to interact in the order drawn? Are you omitting some relevant details? $\endgroup$
    – Glen_b
    Apr 6, 2013 at 11:13
  • $\begingroup$ @Glen_b These are just examples. I want to understand this theoretically, there is no current application. $\endgroup$
    – user14650
    Apr 6, 2013 at 11:15

2 Answers 2

2
$\begingroup$

Flip a coin. If its heads, draw a male first. If its tails draw a female first. Then draw someone of the opposite sex.

$\endgroup$
2
$\begingroup$

According to me those are the same strategies. But I don't have a rigorous proof. (2) and (3) might be a tad less computationally efficient though since they don't guarantee success in two draws.

Why not have two urns instead (odd and even) and draw simultaneously one from each? Whether to draw from one set or the other first could be decided by a 0,1 random integer, eliminating your sequence / predictability concerns?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy