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Chapter 11: Problem 1

In Exercises 1-6, you are dealt one card from a 52-card deck. Find the probability that you are not dealt an ace.

Short Answer

Expert verified
The probability that you are not dealt an ace is \(\frac{12}{13}\).

Step by step solution

01

Identifying Total Cards and Aces

In a standard 52-card deck, there are 4 aces. Since we're finding the probability of not being dealt an ace, we want to find the amount of non-Ace cards, which is 52 - 4 = 48.
02

Calculating Probability

Probability is calculated by taking the total number of successful outcomes (in this case, being dealt a non-Ace card) divided by the total number of possible outcomes. So the probability of being dealt a non-Ace card is \(\frac{48}{52}\) or \(\frac{12}{13}\).

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Key Concepts

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

Counting Principles
Counting principles are basic rules that help us determine the number of ways we can arrange or choose items. In this exercise, we use principles of counting to understand card probabilities. Here's a helpful breakdown:
  • First, identify the total number of items, which in this case is 52 cards.
  • Next, determine the specific group or category you're interested in, such as the 4 aces in the deck.
  • Subtract the number of specific items from the total number to find non-Ace cards. Here, we have 48 non-Ace cards.
  • These principles guide us to understand and calculate probabilities.
Counting principles are the foundation for computing probabilities as they help us make sense of all possible outcomes.
Card Deck
A standard card deck is an essential concept in probability questions. Understanding its structure is key. Here's what you need to know:
  • A standard deck has 52 cards.
  • There are 4 suits: hearts, diamonds, clubs, and spades.
  • Each suit has 13 cards, including numbered cards from 2 to 10, and face cards: jack, queen, king, and ace.
  • Understanding the breakdown helps us assess probabilities based on the card types and suits we are interested in.
Knowing the composition of a deck ensures accurate calculations in card-related probability problems.
Probability Calculation
Calculating probability involves understanding the likelihood of an event happening. Probability is expressed as a fraction or ratio.
To calculate probability:
  • Identify the number of successful outcomes. In this problem, a successful outcome is drawing a non-Ace card, which is 48 cards.
  • Determine the total number of possible outcomes, here 52 cards.
  • Use the formula: \( \text{Probability} = \frac{\text{Number of Successful Outcomes}}{\text{Total Number of Possible Outcomes}} \)
  • For our problem, the probability of drawing a non-Ace card is \( \frac{48}{52} \), which simplifies to \( \frac{12}{13} \).
This calculation tells us there's a high chance of getting a non-Ace card when you select randomly from the deck.

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Most popular questions from this chapter

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