Question

Give the probability, as a percentage, of picking the indicated card from a deck. Face card

Short answer

Answer: The probability of selecting a face card from a standard deck of 52 cards is approximately 23.08%.

Step-by-step solution

Identify the number of face cards in a standard deck

There are 4 suits in a deck (hearts, diamonds, clubs, spades), and for each suit, there is one King, one Queen, and one Jack. So, there are 3 face cards in each suit, making a total of 3 × 4 = 12 face cards in a standard deck.

Identify the total number of cards in a standard deck

A standard deck has 52 cards, with each suit having 13 cards (Ace through King).

Calculate the probability of selecting a face card

To find the probability of selecting a face card, we divide the number of face cards by the total number of cards in the deck: \( \text{Probability} = \frac{\text{Number of face cards}}{\text{Total number of cards}} = \frac{12}{52} \)

Convert the probability to a percentage

To convert the probability into a percentage, multiply the result by 100: \( \text{Percentage} = \text{Probability} \times 100 = \frac{12}{52} \times 100 \)

Simplify the expression to get the percentage

Simplify the fraction and then multiply by 100 to get the percentage: \( \text{Percentage} = \frac{12}{52} \times 100 = \frac{3}{13} \times 100 = 23.08\% \) Thus, the probability of picking a face card from a deck is approximately 23.08%.

Key concepts

Deck of Cards

A standard deck of cards is a crucial tool in understanding probability through simple and tangible examples. It contains a total of 52 cards. These 52 cards are divided into four suits: hearts, diamonds, clubs, and spades. Each of these suits has 13 cards, ranging from Ace to King.

A standard deck, being so uniform and evenly divided, helps beginners easily grasp the concepts of probability. Each suit contains the same kinds of cards: numbers (2 through 10) and face cards (like Jack, Queen, and King). Dealing with this structure smoothly introduces students to probability calculations since every card has an equal chance of being drawn. It becomes simpler to calculate due to its predictable and balanced nature.

When learning probability, understanding the structure of a deck is foundational. It sets the stage for calculating probabilities and understanding the importance of total possibilities when evaluating chances.

Face Cards

Face cards are specific cards in a deck and play an essential role in probability problems. They are the Jack, Queen, and King of each suit.

In a standard deck, there are four suits, and each, as mentioned, has one of each face card. This means there are:

• 1 Jack in hearts, diamonds, clubs, and spades
• 1 Queen in hearts, diamonds, clubs, and spades
• 1 King in hearts, diamonds, clubs, and spades

Making a total of 12 face cards in the entire deck.

Understanding the count and distribution of face cards helps when calculating specific probabilities, such as drawing a face card. It's a smaller subset of the entire deck, making students appreciate the role subsets play in probability calculations.

Percentage Calculation

Converting probabilities into percentages is a skill that simplifies understanding and communication of likelihoods.

To determine the percentage of a probability, you start with the probability fraction. For instance, if you know there are 12 face cards in a deck of 52 cards, the probability of drawing a face card is the fraction \( \frac{12}{52} \).

Next, to convert this probability to a percentage for better clarity, you multiply the fraction by 100. This step transforms our fraction into a percentage:

• First, simplify the fraction \( \frac{12}{52} \) to \( \frac{3}{13} \).
• Then, \( \frac{3}{13} \times 100 \approx 23.08\% \).

This percentage indicates the likelihood of drawing a face card in an understandable form. Turning probabilities into percentages is crucial as it makes probabilistic concepts more accessible and practical for daily applications.