Answer
\[P(A\cup B)=\frac{2}{3}\].
Work Step by Step
Let A be the event that the number is divisible by 2 and let B be the event that the number is divisible by 3.
The possible outcomes of event A and B are:
\[\begin{align}
& A=\{2,4,6,8,10,12,16,18,20,22,24\} \\
& B=\{3,6,9,12,15,18,21,24\} \\
\end{align}\]
\[A\cap B=\{12,18,24\}\]
\[\begin{align}
& P(A)=\frac{11}{24} \\
& P(B)=\frac{8}{24} \\
& P(A\cap B)=\frac{3}{24} \\
\end{align}\]
Hence,
\[\begin{align}
& P(A\cup B)=P(A)+P(B)-P(A\cap B) \\
& P(A\cup B)=\frac{11}{24}+\frac{8}{24}-\frac{3}{24} \\
& P(A\cup B)=\frac{16}{24} \\
& P(A\cup B)=\frac{2}{3} \\
\end{align}\]
The required probability is \[\frac{2}{3}\].
