Answer
53 outcomes
Work Step by Step
Let A and B be any two events defined on a sample space S.
We have given that,
\[N(S)=120\]
\[N(A\cap {{B}^{C}})=15\]
\[N({{A}^{C}}\cap B)=50\]
\[N(A\cap B)=2\]
We have to determine the number of outcomes belonging to neither A nor B; that means \[N{{(A\cup B)}^{C}}\].
We draw the Venn diagram for \[{{(A\cup B)}^{C}}\]
From the diagram we can write \[{{(A\cup B)}^{C}}\]as:
\[\begin{align}
& N{{(A\cup B)}^{C}}=N(S)-N(A\cap {{B}^{C}})-N({{A}^{C}}\cap B)-N(A\cap B) \\
& N{{(A\cup B)}^{C}}=120-15-50-2 \\
& N{{(A\cup B)}^{C}}=53 \\
\end{align}\]
Therefore, 53 outcomes belong to neither A nor B.
