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Chapter 17: Problem 2

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

Short Answer

Expert verified
Answer: The probability of picking the King of Hearts from a deck of 52 playing cards is approximately 1.92%.

Step by step solution

01

Identify the total number of cards in the deck

A standard deck of playing cards has 52 cards, with 13 cards in each of the four suits: Hearts, Diamonds, Clubs, and Spades.
02

Identify the desired outcome

In this problem, the desired outcome is drawing the King of Hearts. There is only one King of Hearts in the deck, so there is one desired outcome.
03

Calculate the probability of the desired outcome

The probability of an event is calculated by dividing the number of desired outcomes by the total number of possible outcomes. In this case, there is only one desired outcome (King of Hearts), and there are 52 total cards in the deck. Thus, \(P(\text{King of Hearts}) = \frac{\text{Number of Desired Outcomes}}{\text{Total Number of Possible Outcomes}} = \frac{1}{52}\)
04

Convert the probability to a percentage

To convert the probability to a percentage, simply multiply the probability by 100: Percentage = Probability * 100 Percentage = \(\frac{1}{52} * 100 = \frac{100}{52} \approx 1.92\%\) Therefore, the probability of picking the King of Hearts from a deck is approximately 1.92%.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Probability Calculation
Calculating probability is about finding how likely an event is to happen. In a deck of cards, this is simply the chance of drawing a particular card. Start by identifying the total number of possible outcomes. For playing cards, that's 52, since a standard deck has 52 cards. Then, figure out how many of those cards meet your specific goal (like drawing the King of Hearts). In this situation, there is only one King of Hearts in the deck. The probability calculation formula is:
  • Probability = \( \frac{\text{Number of Desired Outcomes}}{\text{Total Number of Possible Outcomes}} \)
Here, you have one desired outcome and 52 possible outcomes, resulting in a probability of \( \frac{1}{52} \). This simple division tells you the basic chance of the event occurring.
Percentage Conversion
To make probability easier to understand, we often convert it into a percentage. People generally find percentages more relatable than fractions. To convert a probability to a percentage, multiply it by 100.
  • Percentage = Probability \( \times 100 \)
This formula turns the fraction \( \frac{1}{52} \) into a percentage. Multiplying gives you \( \frac{100}{52} \), which is approximately 1.92%. This conversion means there is about a 1.92% chance of picking the King of Hearts from a deck. Converting probabilities to percentages is a handy way to communicate likelihood.
Playing Cards Probability
Understanding the probability of drawing specific cards from a deck involves knowing the card structure. A standard deck has 4 suits: Hearts, Diamonds, Clubs, and Spades, each with 13 cards. When calculating probability, keep in mind the unique structure, sense of each suit, and rank.
  • For example, there are 4 Kings in a deck, one from each suit.
  • Each type of card, like the King, Queen, or Ace, only appears four times.
Knowing there is only one King of Hearts, you know it's a unique card within this structure. This knowledge directly influences the \( \frac{1}{52} \) probability of drawing that specific card. This understanding of the deck is crucial to solving playing card probability problems effectively.

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Most popular questions from this chapter

Find the mean of \(1,2,3, \ldots, n,\) if \(n\) is (a) 3 (b) 4 (c) 5 (d) 6 (e) \(2 \mathrm{k}\) (f) \(2 \mathrm{k}+1\)

Find the mean and standard deviation for each of the following data sets. (a) 1,2,3,4,5,6,7 (b) 4,4,4,4,4,4,4 (c) 2,2,4,4,4,6,6

Find \(\bar{a}\). $$ a_{i}=i / 2 \text { and } i=1, \ldots, 5 $$

A sample of 20 frogs has a total weight of \(W\) grams. (a) What is the mean weight (in grams per frog) of the sample? (b) One of the frogs has been mis-weighed. Instead of \(x\) grams, its weight is \(y\) grams. What is the corrected mean weight of the sample?

The probability expressions refer to drawing a card from a standard deck of cards. State in words the meaning of the expression and give the probability as a fraction. \(P(\) King \(\cap\) Red \()\)
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