Two absent minded room-mates A and B forget their umbrella’s in some way or another. A always takes his umbrella when he goes out of his home, while B forgets to take his umbrella with probability  $\frac{1}{2}$. Each of them forgets his umbrella at a shop with probability  $\frac{1}{4}$. After visiting three shops they return home. Probability that 

	COLUMN-I		COLUMN-II
A)	Both umbrellas, are in the home	P)	$\frac{4366}{8192}$
B)	Only one umbrella, in the home	Q)	$\frac{2457}{8192}$
C)	B has lost his umbrella given that there is only one, umbrella in the home	R)	$\frac{999}{4366}$
D)	A has lost his umbrella given that there is only one umbrella, in the home	S)	$\frac{3367}{4366}$
		T)	$\frac{1367}{8192}$
		U)	$\frac{5735}{8192}$