Re: DSE 2010 - Q.1

Posted by Amit Goyal on May 27, 2011; 6:20pm
URL: http://discussion-forum.276.s1.nabble.com/DSE-2010-Q-1-tp6411727p6412054.html

A number say X1 is chosen at random from the set {1,2}. Then a number say X2 is chosen at random from the set {1,X1}. The probability that X1=2 given that X2=1 is

a) 1
b) 1/2
c) 1/3
d) 1/4

Pr(X_1=2|X_2=1)=Pr(X_1=2,X_2=1)/Pr(X_2=1) = (Pr(X_2=1|X_1=2)Pr(X_1=2))/(Pr(X_2=1|X_1=2)Pr(X_1=2)+Pr(X_2=1|X_1=1)Pr(X_1=1))
=((0.5)(0.5))/((0.5)(0.5)+(1)(0.5))=1/3