# Actual Real World Probability Problem

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• Aug 3rd 2010, 02:52 AM
LeFromage
Actual Real World Probability Problem
When I was doing my maths degree, I often pondered what the actual uses were for many of the things we did....

Now i've come across a probability question as part of my work, but my brain has officially left the building!

It looks like fairly basic probability stuff, which is quite embarrassing for me especially after dealing such gems as stochastic modelling while a student! Here's a broken down version of the question;

"I have 3 different items in a barrel, A, B and C. They are evenly mixed in the barrel (ie: 1/3 prob of picking each) but are not replaced when they are picked, so this probability will change as we take items out.
For simplicity assume there are 1000 of each item in the barrel to start with, though this number will be subject to change, so the solution should be clearly manipulable to change the input values.

* What is the chance of getting 15 and then 16 items the same?
* What is the chance of not getting at least 3A, 1B and 1C, after both 15 and 16 selections from the barrel."

I've managed to produce a spreadsheet with a changeable input for the number of units which calculates the chance of getting 15 (one in 15.4m) and then 16 (one in 46.7m) of all the same item, but that's as far as I've got!

Should part 2 be as easy as I think it looks, ie: nCr and some conditional formulae? I think perhaps I'm confusing myself. Doesn't help that my memory has become full of P&L's and balance sheets.

I'm considering making the assumption that the probability stays at 1/3 for picking the items, as there are so many items in there, which will hopefully make solving it a lot easier.

Solutions / detailed reminders would be much appreciated!

Thanks,
• Aug 3rd 2010, 04:28 AM
CaptainBlack
Quote:

Originally Posted by LeFromage
When I was doing my maths degree, I often pondered what the actual uses were for many of the things we did....

Now i've come across a probability question as part of my work, but my brain has officially left the building!

It looks like fairly basic probability stuff, which is quite embarrassing for me especially after dealing such gems as stochastic modelling while a student! Here's a broken down version of the question;

"I have 3 different items in a barrel, A, B and C. They are evenly mixed in the barrel (ie: 1/3 prob of picking each) but are not replaced when they are picked, so this probability will change as we take items out.
For simplicity assume there are 1000 of each item in the barrel to start with, though this number will be subject to change, so the solution should be clearly manipulable to change the input values.

* What is the chance of getting 15 and then 16 items the same?
* What is the chance of not getting at least 3A, 1B and 1C, after both 15 and 16 selections from the barrel."

I've managed to produce a spreadsheet with a changeable input for the number of units which calculates the chance of getting 15 (one in 15.4m) and then 16 (one in 46.7m) of all the same item, but that's as far as I've got!

Should part 2 be as easy as I think it looks, ie: nCr and some conditional formulae? I think perhaps I'm confusing myself. Doesn't help that my memory has become full of P&L's and balance sheets.

I'm considering making the assumption that the probability stays at 1/3 for picking the items, as there are so many items in there, which will hopefully make solving it a lot easier.

Solutions / detailed reminders would be much appreciated!

Thanks,

By getting 15 do you mean in 15 draws you 15 the same? If so your spreadsheet is wrong the chance of getting 15 of the same type in a row is ~1 in 5 million (it is about three times as likely as getting 15 A's in a row because we can have 15 As, or 15 Bs or 15 Cs in a row.

As a first cut at this I would assume the probabilities do not change with each draw.

CB
• Aug 3rd 2010, 04:57 AM
LeFromage
Good point, CB! It clearly has been too long since my mind tasted a mathematical challenge! It was indeed 15/15 and then 16/16 attempts I meant, yes.

I did some more digging and found single variable probs. using binomial calculations gave me the chances of getting less than 3(<=2) A's in 16 picks from the barrel as ~ 5.9%, and hence no B's (<=0) as being 0.15% (therefore same for no C's) - now it feels to me like all that should happen next is plugging these in to a formula, but I can't find a suitable one...