A urine test, the VMA test

Question

Neuroblastoma is a rare, serious, but treatable disease. A urine test, the VMA test, has been developed that gives a positive diagnosis in about 70 % of cases of neuroblastoma. It has been proposed that this test be used for large-scale screening of children. Assume 300,000 children are to be tested, of whom 8 have the disease. We are interested in whether or not the test detects the disease in the 8 children who have the disease.

Find the probability that

a) all eight cases will be detected

I have calculated that $1 \cdot (0,7)^{8} \cdot (1 - 0,7)^{0} = 5.8 \% $

b) only one case will be missed

And here I have $8 \cdot (0,7)^{7} \cdot (1 - 0,7)^{1} = 19.8 \% $

c) two or more cases will be missed

But how should I calculate this?

Answer 1

Hint : Is there another possibility to

1. all eight cases will be detected ;
2. only one case will be missed ;
3. two or more cases will be missed ?