The probability that a card drawn from a pack of $52$ cards will be a diamond or a king, is

### Concept & Probability of Non-Mutually Exclusive Events When calculating the probability of event $A$ or event $B$, we add their individual probabilities and subtract the probability of their intersection. $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ ### Step-by-Step Solution * **Total Outcomes:** A deck has $52$ cards. * **Event A (Diamond):** There are $13$ diamonds. $P(\text{Diamond}) = \frac{13}{52}$. * **Event B (King):** There are $4$ kings. $P(\text{King}) = \frac{4}{52}$. * **Intersection (King of Diamonds):** There is $1$ card that is both a diamond and a king. $P(\text{Diamond} \cap \text{King}) = \frac{1}{52}$. * **Calculation:** $P(\text{Diamond} \cup \text{King}) = \frac{13}{52} + \frac{4}{52} - \frac{1}{52} = \frac{16}{52}$. * Simplify the fraction: $\frac{16 \div 4}{52 \div 4} = \frac{4}{13}$. ### Exam Strategy & Shortcut Mentally count the distinct winning cards: $13$ diamonds $+ 3$ non-diamond kings = $16$ cards. Result = $\frac{16}{52} = \frac{4}{13}$. This avoids overcounting entirely. ### Common Pitfall Adding $13$ and $4$ to get $17$ total outcomes without considering that the King of Diamonds was counted twice. ### Final Answer Therefore, the correct answer is **$\frac{4}{13}$**.