Blood testing for disease in groups

[peterchi]

This is a question from my probability homework, and someone please tell me if it's bad form to ask for homework help here (it's completely allowed in terms of my class -- we're allowed to work in groups and get help from anyone and anywhere). But if it's bad for this forum then please let me know and I won't do it again.

On to the question --

To determine whether or not they have a certain disease, 100 people are to have their blood tested. However, rather than testing each individual separately, it has been decided first to group the people into groups of 10. The blood samples of the 10 people in each group will be pooled and analyzed together. If the test is negative, one test will suffice for the 10 people. If the pool is positive, then each of the 10 people will be individually tested. Assume that the probability of disease is 10% for all people, independently of each other. Compute the distribution of the number of tests to be performed along with the expected value and variance.

So... I know that each group of 10 people has a .9^10 probability of testing negative, meaning just one test will suffice. And then with probability 1-.9^10, it will require 11 tests (1 for the whole group and then 10 individually). But I'm not really sure where to go from here.

Thanks in advance.