For the Math Guys

[sturrock]

Need some help with this....... If you have 2 sets of balls with the numbers 1,2,3, written on each of them You put each set into a bucket, what are the chances of pulling the same numbers out in the same order e.g. 3,1,2.   3,1,2. out of each bucket.
Now if you had 18 balls in each bucket with1,2,3, on each of them and you pick three balls out of each Bucket again at the same time, what would the odds be to pick exactly the same numbers out of each bucket at the same time? e.g. 2,3,1   2,3,1 Would there be a difference or would the odd to do this be the same as doing it with just 3 balls in each bucket?  Basically what I am asking the more balls the more unlikely it is to pick the same numbers out in the same order from each bucket ............
Hope you understand
Thanks

[Scarface]

The odds of picking the same 3 balls out of the 2nd bucket would be 1 in 27 (3^3).  I'm assuming that the odds would not change if you had 18 or even a million balls, as long as both buckets were equal

[sturrock]

Thanks SCARFACE 

[Scarface]

I think I get why you ask.  The odds would not change, but I wonder if the variance would.  There have been millions trial tested that shows a dozen can go missing for up to 35 times.  But, I wonder.  What if each dozen contained 100 numbers...would the million trial run show worse results, even though the probability is the same.

[sturrock]

What if you have 6 balls in each bucket, numbered 1 through to 6 and pick them out at the same time, what would be the chances of say picking out the same numbers from each bucket at the same time? And what would be the difference if you put the balls back into the bucket after every pick, or after each pick did not put them back???     

[Blue_Angel]

I think I get why you ask.  The odds would not change, but I wonder if the variance would.  There have been millions trial tested that shows a dozen can go missing for up to 35 times.  But, I wonder.  What if each dozen contained 100 numbers...would the million trial run show worse results, even though the probability is the same.

The probability remains the same but variance would change according the total possible outcomes.
My hypothesis was similar and I've tried to prove it but my limited testing disproved it rather than proved it.
My experiment was with a coin flip (head - tails) VS 52 cards of a deck (36 red - 36 black).
So my hypothesis support that even when there is even chances for both sides to occur, on the case which more elements represent each side it should be more "streaky", but without affecting the overall totals in regards with the law of large numbers.
Therefore a difference on the distribution, not in the totals expectancy/probability.
I've contacted 100 consecutive trials from each and the testings were far from conclusive.

[Blue_Angel]

My experiment was with a coin flip (head - tails) VS 52 cards of a deck (36 red - 36 black).

I want to correct myself, it's 26 black to 26 red cards! 

[Blue_Angel]

What if you have 6 balls in each bucket, numbered 1 through to 6 and pick them out at the same time, what would be the chances of say picking out the same numbers from each bucket at the same time? And what would be the difference if you put the balls back into the bucket after every pick, or after each pick did not put them back??? 

Regarding your first question;
1 out of 6 for any number to be drawn out of 1 bucket equals 6 multiplied by 6 of the second bucket equals 36, thus 1 in 36 chance to draw the exact same number out of both buckets simultaneously.
This is valid when you constantly draw 1 single number out of 6 possible, if we would not put back the drawn numbers then the probability would be increasingly higher as we drew more numbers out of both buckets.

If we put it in perspective, by betting ANY line on 2 different roulette tables then it would have the above mentioned chance for the same to happen on BOTH.

The same chance would have a SPECIFIC line coming 2 times in a row (6 x 6 = 36) for 1 table.

On 2 different tables and expecting for both of the tables to win would have the same chance as expecting 1 win for 1 table.

But if we were betting for EITHER to win on 2 different tables then we would have double the chance.

For a SPECIFIC line of 6 numbers there is 1/6 probability or 16.66% (disregarding 0) to occur, for ANY line of 6 numbers to hit twice in a row has 1/6 or 16.66% chance as well.

[sturrock]

Thanks, BLUE_ANGEL

[Scarface]

The odds of red/black are 50/50 (not counting zero).  There's alot of talk on here about the limits of randomness.  Million spin trials show that worse case an even chance can go missing for is around 25 spins....BUT, what if there were more numbers on the wheel?  What if there were 1000 reds and blacks?  The odds would be the same, but would the the million spin trial show worse results?