4. A blood bank is screening a large population of donations for a particular virus. Suppose 5% of the blood
donations contain the virus. Suppose you randomly select 10 bags of donated blood to screen. You
decide to take a small amount from each of the bags and pool these all together into one sample. If that
sample shows signs of the virus, you then test all of the original 10 bags individually. If the combined
sample does not contain the virus, then you are done after just the one test.
a. Determine the expected number of tests to screen 10 bags of donated blood using this strategy.
b. Does this appear to be an effective strategy? Explain how you know.

Given that a blood bank is screening a large population of donations for a particular virus. Suppose 5% of the blood donations contain the virus. Suppose you randomly select 10 bags of donated blood to screen. You ecide to take a small amount from each of the bags and pool these all together into one sample. If that sample shows signs of the virus, you then test all of the original 10 bags individually. If the combined sample does not contain the virus, then you are done after just the one test.

Probability for doing individual 10 bags= Prob of atleast one having virus in 10

Let X be the no of bags having virus in 10

X is binomial since constant prob and two outcomes

p = 0.05 and n =10

Probability of atleast one having virus in 10 = 1-P(0)

= 1-0.95^10

= 0.4013

Again each group of 10 bags, say Y is binomial with constant probability of requiring individiaul tests.

Expected no of tests to screen 10 bags of donated blood using this strategy = np = 0.4013n where n = no of 10 bags

b) Yes effective because time is saved for individually doing and also prob of getting no virus is 0.5987 more than 50% hence worth trying