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Chapter 10: Problem 24

If a card is drawn from a standard deck of 52 cards, what is the probability that it is a heart?

Short Answer

Expert verified
The probability of drawing a heart from a standard deck of 52 cards is 0.25.

Step by step solution

01

Identify the Total Number of Outcomes

In this case, the total number of outcomes is equivalent to the total number of cards in the deck, which is 52.
02

Identify the Number of Favorable Outcomes

The number of favorable outcomes is the number of hearts in the deck. There are 13 hearts in a standard deck.
03

Calculate the Probability

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.\[ Probability = \frac{number\, of\, favorable\, outcomes}{total\, number\, of\, outcomes} = \frac{13}{52} = 0.25 \] Therefore, the probability of drawing a heart from a standard deck is 0.25.

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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 comprised of 52 individual cards, and it forms the basis for many probability problems. Understanding the composition of the deck is crucial when calculating probabilities. Here鈥檚 a quick breakdown:
  • There are four suits: hearts, diamonds, clubs, and spades.
  • Each suit contains 13 cards, which consist of numbers 2 through 10, as well as a Jack, Queen, King, and Ace.
  • Half of the cards (26) are considered red (hearts and diamonds) and the other half are black (clubs and spades).
Knowing these details will help in identifying the total number of outcomes and the favorable outcomes in probability problems involving a deck of cards.
Favorable outcomes
When determining the probability of drawing a specific card or suit from a standard deck, it is important to identify the favorable outcomes. In probability terms, these are the outcomes that meet the specific criteria of the event you are examining.
  • For example, if the task is to find the probability of drawing a heart, then the number of favorable outcomes is the number of heart cards in the deck.
  • In a standard deck, there are 13 hearts, which are specifically: Ace of Hearts, 2, 3, 4, 5, 6, 7, 8, 9, 10 of Hearts, Jack, Queen, and King of Hearts.
Identifying these favorable outcomes is essential because it allows you to calculate the probability of an event by comparing favorable outcomes to the total possible outcomes.
Total number of outcomes
In probability, the total number of outcomes refers to all possible outcomes of an event. For instance, when drawing a card from a standard deck, you have a total of 52 possible outcomes because the deck contains 52 cards.
  • These outcomes include every single card in the deck, from the 2 of Hearts to the Ace of Spades.
  • Each outcome is equally likely when the deck is well-shuffled.
Having a clear understanding of the total number of outcomes is a fundamental step in probability calculations, as it serves as the denominator when you calculate the probability of a specific event happening.

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Most popular questions from this chapter

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