Solution Found!
Let S = {1, 2, ... , n} and suppose that A and B are,
Chapter 3, Problem 86P(choose chapter or problem)
Problem 86P
Let S = {1, 2, ... , n} and suppose that A and B are, independently, equally likely to be any of the 2n subsets (including the null set and S itself) of S.
(a) Show that
Show that .
Questions & Answers
QUESTION:
Problem 86P
Let S = {1, 2, ... , n} and suppose that A and B are, independently, equally likely to be any of the 2n subsets (including the null set and S itself) of S.
(a) Show that
Show that .
ANSWER:
Step 1 of 2
Let, S = {1, 2,....n} and A and B are independent, equally likely to be any of the subsets of S.
a.) The claim is to show that P{A= (
The are total subsets of S. thus P(N(B) = i) =
.
The set A can be any of the subsets of S. Since B has i elements to have A
B means that all the elements of A must actually also be elements of B.
Thus A must be one of the subsets of B and we have
P(N(B) = i) = .
Then, P(E) =
=
=
=
= (
Hence, P{A= (
.