[Dude]

I haven’t had a probability class in a while and I’ve lost most of my textbooks after a recent move.  I’m trying to confirm a prediction.  Let’s say I have a bucket with 1,000,000 balls in it.  940,000 balls have the number 6, 50,000 balls have the number 7, 49,000 balls have the number 8 and 1,000 balls have the number 9.  If I extract two balls at a time with an extractor, would the probability of pulling out two 9’s simply be 1,000*1,000 / 1,000,000*1,000,000 or 1 x 10-6 and two sixes be 940,000*940,000 / 1,000,000*1,000,000 or 88.36 %?

I’m trying to apply this to the chemical reaction of a monofunctional chemical to a difunctional chemical (ie a mixture of 94 % 1-bromohexane, 5 % 1-bromoheptane, 4.9 % 1-bromooctane and 0.1 % 1-bromononane reacting with p-xylene – assumption of equal reactivity- how much 1,4-didecylbenzene (the product of p-xylene and bromononane would be obtained?)

Thanks,

[Borek]

1,000*1,000 / 1,000,000*1,000,000

Seems OK to me, although I think more precisely it should be 1000/1000000*999/999999

But I can be wrong, I did these things for the last time 20 years ago.

[Dude]

Thanks,
Good point for batch systems.  In my attempt to remain generic, I noted that I also picked a non-reactive system.  Let's assume p-xylene is actually 1,4-dithiobenzene if there are any other takers.

[plu]

A-ha, the old data management!    The chances of picking out two 9-balls from your bucket there would be 1000C2/1000000C2 where C is the "choose" function.  This converts to Borek's value of 1000x999/1000000x999,999.  Picking out two 6-balls would simply be 940000C2/1000000C2 = 940000x939999/1000000x999,999