Re: Discussion Problems of the Day (14-06-11)

Posted by barkha on Jun 16, 2011; 3:11am
URL: http://discussion-forum.276.s1.nabble.com/Discussion-Problems-of-the-Day-14-06-11-tp6472885p6481585.html

hi shruti,

I am not sure what you exactly mean by addition theorem but you can use the following:
Define
A=No one is selected from the freshman class
B=No one is selected from the Sophomore class
C=No one is selected from the Junior class
D=No one is selected from the Senior class

We are interested in finding probability of intersection of the complements of the above Pr(A' ∩ B' ∩ C' ∩ D') = 1 - Pr(A U B U C U D)
We will use inclusion-exclusion principle to determine the probability of A U B U C U D
Pr(A U B U C U D) = Pr(A) + Pr(B) + Pr(C) + Pr(D) -  Pr(A ∩ B) - Pr(A ∩ C) - Pr(A ∩ D) - Pr(B ∩ C) - Pr(B ∩ D) - Pr(C ∩ D) + Pr(A ∩ B ∩ C) + Pr(A ∩ B ∩ D) + Pr(A ∩ C ∩ D) + Pr(B ∩ C ∩ D) - Pr(A ∩ B ∩ C ∩ D)
Now all of the above on the RHS are easy to get.