This problem continues Example A of Section 4.1.2. a. What is the probability that...

This problem continues Example A of Section 4.1.2.

a. What is the probability that a fragment is the leftmost member of a contig?

b. What is the expected number of fragments that are leftmost members of contigs?

c. What is the expected number of contigs?

Reference

Group Testing

Suppose that a large number, n, of blood samples are to be screened for a relatively rare disease. If each sample is assayed individually, n tests will be required. On the other hand, if each sample is divided in half and one of the halves is put into a pool with all the other halves, the pooled lot can be tested. Then, provided that the test method is sensitive enough, if this test is negative, no further assays are necessary and only one test has to be performed. If the test on the pooled blood is positive, each reserved half-sample can be tested individually. In this case, a total of n + 1 tests will be required. It is therefore plausible, assuming that the disease is rare, that some savings can be achieved through this pooling procedure.