III. HOME WORK PROBLEMS
9. GOAL SOFTENING (4)
There are two classes of designs in the design search space, class A
and B with 5 members in each class. If more convenient, you can think
of an urn containing 10 otherwise identical balls labelled A or
B. There are five A's and five B's which you can see.
We also know the probability that either the top 1 or the top 2 design being
contained in class A is 3/4. Suppose the Good enough set G is
defined as the top-2 designs, and we plan to select 2 balls, i.e., selected
subset size |S| = 2.
- What is the alignment probability P(|G intsc S| >=
1), if S is selected by blind picking?
- If you want to maximize the alignment probability, how do you select
your S (explain why), and what is the alignment probability of
this way of picking S?