Re: Daily question

Posted by Amit Goyal on Feb 22, 2009; 3:18am
URL: http://discussion-forum.276.s1.nabble.com/Daily-question-tp2328964p2366187.html

22 - 24 Feb, 2009

Show by means of numerical example that P(B|A)+P(B|A')
a) may be equal to 1;
b) need not be equal to 1.

Given three events A, B and C such that P(A ∩ B ∩ C) ≠ 0, and P(C|A ∩ B) = P(C|B), show that P(A|B ∩ C) = P(A|B)

Show that P(A ∩ B ∩ C) = P(A).P(B).P(C) does not necessarily imply that A, B and C are all pairwise independent.