Probability and Expected Value problem

Here's the question...

The blood samples of k (k > 1) randomly chosen people is tested for

the presence of virus V . Suppose that 5% of the population has this

virus, and that presence of the virus among different people is independent.

Instead of the traditional ”test each of the k blood samples

separately” method, the following alternative method is proposed:

Mix a little of each of the k blood samples and test for the presence of

virus V in the mixture.

• If virus V is not present - done! (since that means that none of

the k people has the virus)

• If virus V is present, go back and test each of the k blood samples

separately. Let the random variable Y be the number of tests

needed for the alternative methods.

(a) Find PY (y) and E(Y ).

(b) For what values of k is the alternative method more cost effective?

(in the sense that less tests are required, on average)

Thank you