In a standard deck of 52 playing cards, one card is drawn at random. Assuming that each of the 52 cards is equally likely to be drawn, what is the probability that the card drawn is red?

Introduction:
This question tests a very important basic concept in probability related to a standard deck of playing cards. You are asked to calculate the probability that a randomly drawn card is red when all 52 cards are equally likely to be drawn. Understanding this kind of question builds a foundation for more complex probability problems that involve conditional events and combinations.

Given Data / Assumptions:

• We are using a standard deck of 52 playing cards.
• The deck has no jokers or missing cards.
• Each one of the 52 cards is equally likely to be drawn.
• We want the probability that the card drawn is a red card.
• Red cards in a standard deck are hearts and diamonds.

Concept / Approach:
In basic probability, when all outcomes are equally likely, the probability of an event is given by:
Probability of event = (Number of favorable outcomes) / (Total number of possible outcomes) Here, the event is "the card drawn is red." Therefore, we need to count how many red cards are in the deck and divide that by the total number of cards in the deck. A standard deck has two red suits: hearts and diamonds, and each suit has 13 cards.

Step-by-Step Solution:
Step 1: Find the total number of possible outcomes. There are 52 distinct cards in a standard deck, so the total number of possible outcomes is 52.
Step 2: Count the number of favorable outcomes. There are 2 red suits (hearts and diamonds), and each suit has 13 cards. So the total number of red cards is:
Number of red cards = 13 (hearts) + 13 (diamonds) = 26. Step 3: Apply the probability formula. Probability(card is red) = Number of red cards / Total number of cards = 26 / 52. Step 4: Simplify the fraction. Divide numerator and denominator by 26:
26 / 52 = 1 / 2. So the probability that the card drawn is red is 1/2.

Verification / Alternative check:
Another way to think about this is that in a standard deck, exactly half of the cards are red and half are black. Since there are only two colors (red and black) and each color has the same number of cards (26), the chance of drawing either color is equally likely. Therefore, the probability of drawing a red card is 1 out of 2, which again gives 1/2. This confirms our calculation and provides an intuitive check on the answer.

Why Other Options Are Wrong:
2/3: This would suggest that two thirds of the deck is red, which is not true because only half the deck is red and the other half is black.
1/52: This would be the probability of drawing one specific card, such as the ace of hearts, not any one of the 26 red cards.
13/51: This fraction does not correspond to any natural count in a full 52 card deck for this event. It might appear in other card problems but not here.
1/4: This would suggest that only 13 of 52 cards are red, which is incorrect because there are 26 red cards in total.

Common Pitfalls:
A common mistake is to forget the composition of a standard deck and miscount the number of red cards. Some learners confuse the probability of drawing a specific card (1 out of 52) with the probability of drawing any card of a certain color or suit. Others may incorrectly assume that each suit is a color category on its own. Always remember: a standard deck has 4 suits with 13 cards each, and exactly 2 of these suits (hearts and diamonds) are red, giving 26 red cards. Using the basic probability formula correctly avoids these errors.

Final Answer:
The probability that the card drawn from a standard 52 card deck is red is 1/2.