Answer
The following probabilities of the events are arranged from smallest to largest:
\[\begin{align}
& (A\cap B) \\
& [(A\cap B)\cup (A\cap C)] \\
& (A) \\
& (A\cup B) \\
& (S)\text{ } \\
\end{align}\]
Work Step by Step
Let A, B and C be three events defined on a sample space, S.
We want to arrange the probabilities of the events \[(A\cup B),\text{ }(A\cap B),\text{ }A,\text{ }S,\text{ }(A\cap B)\cup (A\cap C)\] from smallest to largest.
Hence we are using Venn diagram.
Since, \[P(S)=1\]
From a Venn diagrams we can see that the order is,
\[\begin{align}
& (A\cap B) \\
& [(A\cap B)\cup (A\cap C)] \\
& (A) \\
& (A\cup B) \\
& (S)\text{ } \\
\end{align}\]
