We help IT Professionals succeed at work.

Probability question

Castaway78 asked
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!
Watch Question

Awarded 2010
Top Expert 2013
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
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
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



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!