Let, #U_1=#the Event that the Urn No. 1 is selected,
#U_2=#the Event that the Urn No. 2 is selected,
#W=#the Event that a White Ball is selected from the selected
Urn.
We see that, #U_1 and U_2# are mutually exclusive & exhaustive
events, and, #W# is going to occur relative to either of #U_1, U_2#.
Accordingly, #P(W)=P(U_1)P(W/U_1)+P(U_2)P(W/U_2)...(ast).#
Clearly, #P(U_1)=P(U_2)=1/2..................(1).#
For, #P(W/U_1)#, we understand that the Urn No. 1 has been
selected, and a White Ball has been drawn from it.
In the Urn No. 1, there are, #9W+9Y=18# balls, and #1# ball can
be chosen in #18# ways.
From the Urn No. 1, #1# White ball, out of, #9# can be chosen
in #9# ways.
#:. P(W/U_1)=9/18.................................(2).#
Similarly, #P(W/U_2)=8/11..................(3).#
Using #(1),(2) and (3)# in #(ast)#, we have,
#"The Reqd. Prob.="1/2*9/18+1/2*8/11=27/44.#
Enjoy Maths.!
