One card is drawn at random from a standard pack of 52 playing cards. What is the probability of getting either the queen of clubs or the king of hearts?

Introduction / Context:
This question is a simple probability problem focusing on two specific cards in a standard deck. Rather than dealing with a whole suit or rank, it asks for the chance that a single draw yields one of two particular cards. This highlights the idea of counting individual favourable outcomes in a uniform sample space.

Given Data / Assumptions:

• There is a standard deck of 52 distinct cards.
• We are interested in two specific cards: the queen of clubs and the king of hearts.
• One card is drawn at random from the deck.
• Every card has the same probability of being drawn.

Concept / Approach:
When each outcome in the sample space is equally likely, probability equals favourable outcomes divided by total outcomes. Here, each individual card is one outcome. The favourable outcomes are exactly the two mentioned cards. There is no overlap because a single card cannot be both the queen of clubs and the king of hearts.

Step-by-Step Solution:
Total number of cards in the deck = 52. Favourable cards = queen of clubs and king of hearts, so there are 2 favourable cards. Required probability = favourable outcomes / total outcomes = 2 / 52. Simplify 2 / 52 by dividing numerator and denominator by 2 to obtain 1 / 26.

Verification / Alternative check:
An alternative way to see this is to compute the probability of each card separately and then add them, because the events are mutually exclusive. Probability of queen of clubs = 1 / 52. Probability of king of hearts = 1 / 52. Since both cannot occur together on a single draw, the combined probability is 1 / 52 plus 1 / 52, which equals 2 / 52 or 1 / 26. This matches the combination reasoning.

Why Other Options Are Wrong:
1/52 corresponds to the probability of drawing only one specific card, not one of two specific cards. 1/13 would mean 4 favourable cards, which would be correct for any one rank such as any king, but not just one king and one queen. 1/4 suggests 13 favourable cards, which is far too many for only two particular cards.

Common Pitfalls:
Some learners mistakenly multiply probabilities for the two cards instead of adding them. Multiplication is used for joint occurrence, but here a single card cannot be both the queen of clubs and the king of hearts at the same time. When events are mutually exclusive and we want either one or the other, probabilities should be added, not multiplied.

Final Answer:
The probability of drawing either the queen of clubs or the king of hearts is 1/26.