Fun ways to sample items?

So I work in Quality Assurance and we have to sample 3% of items produced. This is normally done by our system however there are rare occurrences where we have to do it manually.

Right now we have a clear box with 5 pennies and we shake them, slam them down and if all are heads the item is selected. (3.125% chance)

I'm curious if anyone has another fun method we could use to do this, maybe with dice or something that would give us an even 3% chance.

Generate the randomness on a computer instead of shaking a box you fucking imbecile not wasting energy sounds like fun to me

Roll two dice, and if both roll 6 (or any predetermined number) test the item (0.0277)

you could use two d10s

Pull a card from a deck of 32 plus one joker, joker selects the item (3.03%).

Judging from shaking pennies in a box you're not bothered by noise, so build a Galton board with a certain number of finish slots, select a slot with a probability of just over 3% as the winning slot, and run a marble down the board for each item.

It has to be at least 3%.

What would be the selection criteria?

That's not bad, I kind of like it... but there is the possibility of the Joker having/gaining a distinguishing mark or something.

That sounds cool, but how do you prove it's chances?

this is a word problem from your homework, fck offf nerd

Nope, this is an actual scenario.

a 0 on one d10 and a 3 on the other

>That sounds cool, but how do you prove it's chances?
If you build it properly, the chances of the ball going right at each stage is 0.5.
Then, the probability of a ball landing in the k-th bin is binomially distributed, i.e. P[N=k] = (N chose k)*0.5^k * (1-0.5)^n-k when the number of bins is n.

The math on that doesn't seem to add up to me for some reason, could you explain it?

Can you show me an example that would give me a 3% selection?

Write some Ruby.

The 11th bin of a 32-bin Galton board will have a probability of 0.0300408527255 of being selected.

This python script will give you a Galton board and bin that results in a selection probability close to 0.03 with any desired accuracy.

def galton(acc):
n = 1
while True:
for k in range(1,n):
p = scipy.special.binom(n,k)*(0.5**k)*(0.5**(n-k))
if abs(p-0.03)

Forgot that Veeky Forums ignores indents without code tags.

I really fucking like this idea, it's just that there has to be such precision in the design, right? Having the first pin slightly to the left could drastically lower the chances of any of the bins on the left being selected.

That being said, I work for a Precision Measurement Equipment lab so we shouldn't have a problem doing this... I just don't want it being brought into question in the future.

Yeah, the probability distribution is only valid for a constant p of 0.5.

roll 2d6 and select the item if you get two 1's, and reroll if you get two 6's or a 5 and a 6. Chances should be 3.03%

Anyone else have some ideas? Maybe the 5 pennies method is the best non-computerized method?