Probability problem

iNCREDiBLE
I'm new to this, so can someone please explain how this problem is solved:

What is the probability that your divisions manning will decrease given that corporation's retention rate?

Corporation retention figures for first-term (0-4 years), second-term (4-8 years), and third-term contracts (8-12 years) were 30%, 46%, and 54% respectively.

Personnel within the division is:
10 first-term individuals
12 second-term individuals
10 third-term individuals

We know the corporations retention figures as they have already occurred, now...what is the probability of attrition within a division within the corporation with regards to this additional information?

Homework Helper
iNCREDiBLE said:
I'm new to this, so can someone please explain how this problem is solved:

What is the probability that your divisions manning will decrease given that corporation's retention rate?

Corporation retention figures for first-term (0-4 years), second-term (4-8 years), and third-term contracts (8-12 years) were 30%, 46%, and 54% respectively.

Personnel within the division is:
10 first-term individuals
12 second-term individuals
10 third-term individuals

We know the corporations retention figures as they have already occurred, now...what is the probability of attrition within a division within the corporation with regards to this additional information?
In each category, an individual either leaves the company or stays with the company with a probability that is known from the retention statistics. You can find the probability of retaining every individual in the division from the product of the probabilities of retaining each of them. The probability of attrition is 1 minus the probability that nobody leaves. If you have studied the binomial distributiuon, you can also treat this problem as a combination of three binomial problems. The probability that all individuals within one category in your division are retained depends on the number of such individuals and the probability of retaining such an individual.