Points to Remember:
- Probability is the likelihood of an event occurring.
- A standard deck of cards has 52 cards.
- Face cards are Jacks, Queens, and Kings.
Introduction:
This question requires a factual and analytical approach to determine the probability of drawing a face card from a standard deck of 52 playing cards. Probability is a mathematical measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. In this case, we are calculating the probability of a specific event (drawing a face card) from a defined sample space (a deck of 52 cards).
Body:
1. Defining Face Cards and Sample Space:
A standard deck of 52 playing cards consists of four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. Face cards are defined as Jacks, Queens, and Kings. Therefore, there are three face cards per suit.
2. Calculating the Number of Face Cards:
Since there are four suits and three face cards per suit, the total number of face cards in the deck is 4 suits * 3 face cards/suit = 12 face cards.
3. Calculating the Probability:
Probability is calculated as the ratio of the number of favorable outcomes (drawing a face card) to the total number of possible outcomes (drawing any card from the deck).
Probability (Face Card) = (Number of Face Cards) / (Total Number of Cards)
Probability (Face Card) = 12 / 52
4. Simplifying the Probability:
The fraction 12/52 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4.
Simplified Probability (Face Card) = 3 / 13
5. Expressing the Probability:
The probability of drawing a face card is 3/13. This can also be expressed as a decimal (approximately 0.23) or a percentage (approximately 23%).
Conclusion:
The probability of drawing a face card from a standard deck of 52 cards is 3/13, or approximately 23%. This calculation demonstrates a fundamental concept in probability theory: determining the likelihood of an event based on the ratio of favorable outcomes to the total number of possible outcomes. Understanding probability is crucial in various fields, including statistics, risk assessment, and decision-making. This simple example highlights the power of mathematical reasoning in analyzing seemingly random events and making informed predictions. Further exploration of probability theory can lead to a deeper understanding of uncertainty and its management in various aspects of life.
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