One card is drawn at random from a standard pack of 52 playing cards, each card being equally likely. What is the probability that the card drawn is an ace?

Introduction / Context:
This is one of the simplest and most common probability questions asked with playing cards. It focuses on finding the probability that a single card drawn at random from a full deck is an ace. The key is to know how many aces there are in the deck and then use the basic probability formula based on equally likely outcomes.

Given Data / Assumptions:

• A standard deck contains 52 cards in total.
• There are 4 suits: hearts, diamonds, clubs and spades.
• Each suit contains exactly one ace, so there are 4 aces in the deck.
• One card is drawn at random, and all 52 cards are equally likely to be drawn.
• We want the probability that the selected card is an ace.

Concept / Approach:
In a uniform sample space where each card has equal probability, the probability of drawing a card with a specific property is equal to the number of cards with that property divided by the total number of cards. Here the property is being an ace, and we know there are four such cards in the deck.

Step-by-Step Solution:
Number of aces in a standard deck = 4. Total number of cards = 52. Required probability of drawing an ace = favourable outcomes / total outcomes. So the probability is 4 / 52. Simplify 4 / 52 by dividing numerator and denominator by 4 to obtain 1 / 13.

Verification / Alternative check:
We can think of this as choosing a card by first choosing a rank and then a suit. There are 13 ranks in the deck, and exactly one of them is the ace rank. So the chance that the chosen card has rank ace is 1 out of 13, which directly gives probability 1 / 13. This reasoning matches our earlier fraction and confirms that the answer is correct.

Why Other Options Are Wrong:
1/12 would correspond to about 4.33 aces in the deck, which is not possible. 1/14 and 1/15 are even smaller and suggest fewer than 4 favourable cards, which again contradicts the structure of a standard deck.

Common Pitfalls:
A typical mistake is confusing aces with face cards and assuming there are more or fewer aces than there really are. Another occasional error is to mix up the total number of cards, for example using 54 when thinking about decks with jokers, even though jokers are not part of a standard 52 card deck in most probability questions. Clarifying deck composition before starting the calculation helps avoid these problems.

Final Answer:
The probability that the card drawn is an ace is 1/13.