One card is drawn from a pack of $52$ cards. What is the probability that the card drawn is either a red card or a king ?

### Concept & Probability of Non-Mutually Exclusive Events When finding the probability of $A$ or $B$ where the events can occur simultaneously, we use the general addition rule: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ ### Step-by-Step Solution * **Total Outcomes:** $n(S) = 52$. * **Event A (Red card):** There are $26$ red cards (hearts and diamonds). $P(\text{Red}) = \frac{26}{52}$. * **Event B (King):** There are $4$ kings in a deck. $P(\text{King}) = \frac{4}{52}$. * **Event A and B (Red King):** There are $2$ red kings (King of Hearts, King of Diamonds). $P(\text{Red} \cap \text{King}) = \frac{2}{52}$. * **Calculation:** $P(\text{Red} \cup \text{King}) = \frac{26}{52} + \frac{4}{52} - \frac{2}{52} = \frac{28}{52}$. * Simplify the fraction: $\frac{28}{52} = \frac{7}{13}$. ### Exam Strategy & Shortcut Instead of formulas, just count the favorable cards using basic set logic: Take all $26$ red cards. Now add any missing kings. The black kings are $2$ extra cards. Total favorable cards = $26 + 2 = 28$. Probability = $\frac{28}{52} = \frac{7}{13}$. ### Common Pitfall Double-counting the overlapping cards (the red kings). If you just add $26 + 4 = 30$, you will get the incorrect answer. ### Final Answer Therefore, the correct answer is **$\frac{7}{13}$**.