A card is drawn from a pack of $52$ cards. The probability of getting a queen of club or a king of heart is

### Concept & Addition Theorem of Probability When two events $A$ and $B$ are mutually exclusive (cannot happen at the same time), the probability of either occurring is the sum of their individual probabilities. $$P(A \text{ or } B) = P(A) + P(B)$$ ### Step-by-Step Solution * **Total Outcomes:** A standard deck has $52$ cards, so $n(S) = 52$. * **Event A (Queen of Club):** There is exactly $1$ queen of clubs in the deck, so $n(A) = 1$. * $P(\text{Queen of Club}) = \frac{1}{52}$ * **Event B (King of Heart):** There is exactly $1$ king of hearts in the deck, so $n(B) = 1$. * $P(\text{King of Heart}) = \frac{1}{52}$ * Since drawing a single card cannot be both a queen of clubs and a king of hearts, the events are mutually exclusive. * **Calculation:** $P(A \text{ or } B) = \frac{1}{52} + \frac{1}{52} = \frac{2}{52} = \frac{1}{26}$. ### Exam Strategy & Shortcut For mutually exclusive, specific individual cards, simply count the total number of winning cards and divide by $52$. Two specific cards = $2/52 = 1/26$. ### Common Pitfall Multiplying the probabilities instead of adding them. Remember that "OR" usually signifies addition for mutually exclusive events, whereas "AND" implies multiplication. ### Final Answer Therefore, the correct answer is **$\frac{1}{26}$**.