I sometimes play lottery. The tickets are $5$ digit numbers, for example $34298$. I always buy a ticket which have $2$ even, $3$ odd numbers on it or vice versa, even though I know that it does not make sense mathematically (or does it?). I would never choose a ticket like $13579$ or $11335$.
What would you prefer?
To make an analogy, imagine that there are many black and white balls in a bag. If you take $5$ balls from the bag it is more likely that you would get some black and some white balls. Similarly if you wrote even numbers on black balls and odd numbers on white balls, more likely you would get some even and some odd numbers.
Is my analogy wrong?