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Magazine Chapter 15: Problem 24
\text { A king is drawn. } \frac{1}{13}
Short Answer
Expert verified
The probability of drawing a king is \( \frac{1}{13} \).
Step by step solution
01
Understanding the Problem
We need to calculate the probability of drawing a king from a standard deck of 52 playing cards. There are 4 suits, each with 13 cards, and each suit contains one king.
02
Count the Total Number of Possible Outcomes
Since we are drawing from a deck of 52 cards, there are 52 possible outcomes.
03
Count the Number of Favorable Outcomes
The favorable outcomes are the cases where a king is drawn. There is 1 king in each of the 4 suits, making a total of 4 kings.
04
Calculate the Probability
The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. Thus, the probability of drawing a king is calculated as \( \frac{4}{52} \).
05
Simplify the Fraction
The fraction \( \frac{4}{52} \) can be simplified by dividing the numerator and the denominator by 4, giving \( \frac{1}{13} \). This simplified fraction represents the probability of drawing a king.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Standard Deck of Cards
A standard deck of cards is a familiar tool in probability exercises. A deck consists of 52 cards, which are divided into four suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards, ranging from Ace through King. This structured setup allows us to calculate probabilities based on known possibilities.
When working with probability problems involving a deck of cards, the total number of possible outcomes is typically 52, considering each card could potentially be the outcome.
When working with probability problems involving a deck of cards, the total number of possible outcomes is typically 52, considering each card could potentially be the outcome.
- The four suits are of equal size, each containing 13 cards.
- Each suit follows a traditional rank order, such as Ace, 2, 3, ..., through King.
- Understanding the uniform structure of the deck is essential for correctly setting up and solving probability scenarios.
Favorable Outcomes
In probability, understanding favorable outcomes is crucial. A favorable outcome is simply the event you are interested in.
In the problem about drawing a king, our favorable outcomes are drawing one of the four kings from the deck. Since there are four suits and each suit contains exactly one king:
In the problem about drawing a king, our favorable outcomes are drawing one of the four kings from the deck. Since there are four suits and each suit contains exactly one king:
- The number of favorable outcomes for drawing a king is four.
- Each favorable outcome represents drawing a king from one of the four suits.
Simplifying Fractions
Simplifying fractions in probability is a helpful step that makes understanding the likelihood of an event easier and cleaner.
When calculating probabilities, the result is often a fraction that represents the ratio of favorable outcomes to the total number of possible outcomes. In the case of drawing a king, the probability started as \( \frac{4}{52} \) because there are 4 kings in a deck of 52 cards.
When calculating probabilities, the result is often a fraction that represents the ratio of favorable outcomes to the total number of possible outcomes. In the case of drawing a king, the probability started as \( \frac{4}{52} \) because there are 4 kings in a deck of 52 cards.
- Simplifying means reducing the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
- In \( \frac{4}{52} \), both 4 and 52 can be divided by 4, the GCD, resulting in \( \frac{1}{13} \).
