A fundamental monotonicity in group testing.

The group testing problem is to find by group tests all defectives in a given set of items each of which independently has probability p of being defective. The group testing problem originated with the famous Dorfan's blood testing problem and has since found many industrial applications including a recent one on multiple-access communication. Unfortunately, optimal group testing algorithms are not known in general. In particular, a very plausible conjecture that the expected number of tests should be nondecreasing in p for 0