Q.A card is drawn from a well-shuffled deck of $52$ playing cards. Let $A =$ 'the card is a king' and $B =$ 'the card is a heart'. Are $A$ and $B$ mutually exclusive? Give a reason.

[!TLDR] Check whether $A \cap B$ is empty. [!ANSWER] Not mutually exclusive; $A \cap B = {\text{king …

$A$ = 'the card is a king' has $4$ cards (one king per suit). $B$ = 'the card is a heart' has $13$ cards (all cards of the heart suit). These events are mutually exclusive only if $A \cap B = \phi$, i.e. if no card is both a king and a heart. But the king of hearts is a single card that is simultaneously a king (so in $A$) and a heart (so …

Check directly whether an outcome exists satisfying both conditions simultaneously; a single common outc …

A common mistake is assuming 'king' and 'heart' describe unrelated categories and are therefore automatically mutually exclusive — mutual exclusivity must be checked against the a …