1. ## Binomial Probability Question

100 people are split into 10 groups. Blood sample of every person is then mixed and pooled and then tested for disease. If the test is positive that is at least one person has the disease, all 100 people must be tested separately. We do this for ten groups.

If x is the random variable for the number of blood tests performed in a single group of 100 people, what are the possibilities of y and the probability of each?

Answer is 1 and 101 for the possibilities, but don't understand why?

2. Originally Posted by sankeel
100 people are split into 10 groups. Blood sample of every person is then mixed and pooled and then tested for disease. If the test is positive that is at least one person has the disease, all 100 people must be tested separately. We do this for ten groups.

If x is the random variable for the number of blood tests performed in a single group of 100 people, what are the possibilities of y and the probability of each?

Answer is 1 and 101 for the possibilities, but don't understand why?
I suppose the red y is meant to be an X ....?

If you do 1 test and the test is not positive then you don't do any more tests. So X = 1.

If you do 1 test and the test is positive, then you have to test every person (100 more tests). So X = 1 + 100 = 101.