A single card is drawn at random from a well-shuffled standard deck of 52 playing cards. What is the probability that the card is either a heart or a diamond?

Introduction / Context:
This is another basic probability question with playing cards. The deck is standard and well shuffled, and we want the probability that the drawn card belongs to one of the two red suits, hearts or diamonds. This reinforces understanding of suit structure and simple probability ratios.

Given Data / Assumptions:

• A standard deck of cards has 52 cards.
• There are four suits: hearts, diamonds, clubs, and spades.
• Hearts and diamonds are red suits; clubs and spades are black suits.
• Each suit has 13 cards.
• We want the probability that the card is a heart or a diamond.

Concept / Approach:
The set of hearts and diamonds together forms all red cards in the deck. This is exactly half of the deck. We can either reason directly from symmetry or explicitly count the number of hearts and diamonds and divide by 52.

Step-by-Step Solution:
Number of hearts in the deck = 13. Number of diamonds in the deck = 13. Total favourable cards (hearts or diamonds) = 13 + 13 = 26. Total cards in the deck = 52. Required probability = favourable / total = 26 / 52. Simplify 26 / 52 by dividing numerator and denominator by 26 to get 1 / 2.

Verification / Alternative check:
A symmetry argument provides a quick check. Two of the four suits are hearts and diamonds. Since all suits have equal size and the deck is well shuffled, the chance of drawing a card from any particular pair of suits is exactly 2 out of 4, which equals 1/2. This is consistent with the explicit fraction based calculation.

Why Other Options Are Wrong:
1: This would mean certainty that the card is a heart or diamond, which is not true because it could be a club or spade.
3/4: This would correspond to 39 favourable cards out of 52, which is too many and incorrectly includes black suits.
1/3: This would imply about 17 favourable cards, which does not match the actual count of 26.
None of these: This is incorrect because 1/2 is in the list and is the correct probability.

Common Pitfalls:
Some learners confuse hearts and diamonds with one single suit or incorrectly remember the number of cards in each suit. Others forget that the total deck has 52 cards and miscalculate the fraction. Remembering that there are four suits, each with 13 cards, and that two of them are red, makes the problem straightforward.

Final Answer:
Hence, the probability that the card drawn is either a heart or a diamond is 1/2.