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# Probability question

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Hi all -

I need help figuring out a formula to use.

Here's some sample data.

I have a two groups totalling 30 people. 10 from group A, 20 from group B. Group A is on average 25% complete with thier individual tasks. The Group B is on average 75% complete with thier individual tasks.

I want to know the probability of the next person being 100% ready being from Group A. (eg, "There's a __% chance that the next person ready will be from group A.")

I should note that I do have individual progress statistics... so if average is not what I should be using, I can tweak that.

I hope I explained my situation clearly enough. Let me know if you have any questions.

Thank you!
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Awarded 2010
Top Expert 2013
Commented:
You would need to know the distribution of the data not just the average to figure out this problem.
What you are looking at is a conditional probability. The data you really need is the probability that someone selected from A is 100% done and the probability that someone from B is 100% done.
Those are written as P(100%|A) and P(100%|B).

Then the probability that someone is from A if they are 100% done is written as P(A|100%) and is calculated by P(A|100%) = P(100%|A)*P(A)/P(100%)
where P(100%|A) is the percentage of group A at 100%
P(A) = 10/(10+20)
P(100%) = total_number_at_100% / 30
Awarded 2010
Top Expert 2013
Commented:
The above was calculated using Bayes' rule.
The actual result that I calculated is the probability that a randomly selected person at 100% came from group A.
To actually get the odds that the NEXT person added to the 100% group was from group A, you'd really need more data.

Basically, you want to find the probability that someone from A will go to 100% and the probability that someone from B will go up to 100%. Then you can use those in place of the P(100%|A) and P(100%|B).
Most Valuable Expert 2014
Top Expert 2015
Commented:
besides knowing how % complete is distributed around the average for groups A and B,
you would may also need to know how the distribution evolves with time to get the probability
that a given % complete will become 100% complete in a given time interval.
(if we can know, for example, that if one person is x% complete and another person is y% complete,
where x > y, then the first person will always have a greater % complete than the second,
then the distribution at a given instant would suffice)
Awarded 2010
Top Expert 2013

Commented:
Agreed.

Commented:
Thank you both for your replies. I guess this will be a bit more complex than I had originally hoped. But what you wrote makes sense.

Back to the 'ole drawing board...

Thanks again!