Official solution
Sample space = {00, 01, 02, 03, ..........49} = 50 tickets
n(S) = 50
n(Sum = 8) = { 08, 17, 26, 35, 44 } = 5
n(Product = 0) = { 00, 01, 02, 03, 04, 05, 06, 07, 08, 09, 10, 20, 30, 40 } = 14
\[\therefore\] Probability when product is 0 = P(Product = 0) = \[{14 \over {50}}\]
n(Sum = 8 \[ \cap \] Product = 0) = { 08 } = 1
\[\therefore\] Probability when sum is 8 and product is 0 = P(Sum = 8 \[ \cap \] Product = 0) = \[{1 \over {50}}\]
Required probability,
\[P\left( {{{Sum = 8} \over {Product = 0}}} \right)\]
= \[{{P\left( {Sum = 8 \cap Product = 0} \right)} \over {P\left( {Product = 0} \right)}}\]
= \[{{{1 \over {50}}} \over {{{14} \over {50}}}}\]
=\[{1 \over {14}}\]
\[\therefore\] Option (D) is correct.