Official solution
No of outcome for a die = { 1, 2, 3, 4, 5, 6 }
According to the question,
A = { 4, 5, 6 }
\[\therefore\] P(A) = \[{3 \over 6}\]
B = { 1, 2, 3, 4 }
\[\therefore\] P(A) = \[{4 \over 6}\]
A \[ \cap \] B = { 4 }
So P(A \[ \cap \] B) = \[{1 \over 6}\]
We know, \[P\left( {A \cup B} \right)\] = \[P\left( A \right)\] + \[P\left( B \right)\] - \[P\left( {A \cap B} \right)\]
\[\therefore\] \[P\left( {A \cup B} \right)\] = \[{3 \over 6}\] + \[{4 \over 6}\] - \[{1 \over 6}\] = \[{{7 - 1} \over 6}\] = \[{6 \over 6}\] = 1
\[\therefore\] Option (C) is correct.