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.
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