From a well shuffled standard pack of 52 playing cards, one card is drawn at random.\nWhat is the probability that the card obtained is either a red card or a black card?

Introduction / Context:
In this question we work with a standard pack of playing cards and basic probability. The aim is to understand how to calculate the probability of an event that actually covers the entire sample space, namely drawing either a red card or a black card from a standard deck of 52 cards.

Given Data / Assumptions:

• There is a standard deck with 52 cards.
• There are 26 red cards (hearts and diamonds) and 26 black cards (spades and clubs).
• The deck is well shuffled, so every card is equally likely to be drawn.
• One card is drawn at random.
• We want the probability that the card is red or black.

Concept / Approach:
Probability of an event = (number of favourable outcomes) / (total possible outcomes). Here, the event is "card is red or black". In a standard deck every card is either red or black, so the favourable outcomes are all 52 cards. This is an example of an event that is certain, so its probability is equal to 1.

Step-by-Step Solution:
Total number of cards in the deck = 52 Number of red cards = 26 Number of black cards = 26 Total favourable outcomes (red or black) = 26 + 26 = 52 Probability = favourable / total = 52 / 52 = 1 Thus the required probability is 1, meaning the event is certain to occur.

Verification / Alternative check:
Another way is to note that the sample space consists of all cards. There is no third colour in a standard deck. Therefore every possible draw is favourable to the event. Hence probability must be 1. This matches our calculation above.

Why Other Options Are Wrong:
Option 1/2 suggests only half the deck is favourable, which is incorrect because both colours are included. Option 3/4 would mean only 75 percent of cards are red or black, which is again wrong. Option 1/3 is even smaller and has no connection with the actual card counts.

Common Pitfalls:
A common confusion is to think that red or black is the same as choosing one suit or one colour only. Another mistake is to mix up the idea of "either red or black" with "red or black but not both", which is meaningless here because no card can be both colours at once. Remember that in a standard deck there are no cards that are neither red nor black.

Final Answer:
The required probability that the drawn card is either red or black is 1.