DSE 2010 - Q.1

[Swati Kanodia]

Sir I have a problem in the following question:

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

Sir can you please explain me the answer to the above question as I am getting 1/2 as the answer.

[Amit Goyal]

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

[Swati Kanodia]

Thank you sir..:)))