Q.A die is thrown once. Let $A =$ 'the number is a multiple of $3$' and $B =$ 'the number is even'. Write $A$, $B$ and $A \cap B$ as subsets of the sample space, and state whether $A$ and $B$ are mutually exclusive.

[!TLDR] Build $A$, $B$ from $S=\{1,\dots,6\}$ and check their intersection. [!ANSWER] $A=\{3,6\}$, $B=\{2,4,6\}$, …

$S = \{1,2,3,4,5,6\}$. 'Multiple of $3$': the numbers from $1$ to $6$ that are multiples of $3$ are $3$ and $6$, so $A = \{3,6\}$. 'Even': the even numbers from $1$ to $6$ are $2,4,6$, so $B = \{2,4,6\}$. Intersecting: the only number in both lists is $6$, so $A \cap B = \{6\}$. Since $A \cap B = \{6\} \ne \phi$, the events are NOT mutually exclus …

List $A$ and $B$ explicitly from the sample space, then intersect the two lists dire …

A common mistake is assuming 'multiple of 3' and 'even' are unrelated properties and concluding mutual exclusivity withou …