Homework Help is Here – Start Your Trial Now!
Math
Probability
Each card in a standard deck of cards has a rank and a suit. The cards are ranked from 2 to 10, followed by the 3 face cards: Jack, Queen, King, and the highest ranked card is the Ace, for a total of 13 card ranks. There are four card suits (spades -, clubs hearts -, diamonds -). In total, the deck has 52 cards with a rank and a suit. A casino might use digital cards displayed on a screen, which allows the dealer to deal from a deck with an infinite number of cards. When a card, (e.g., Q♥) is "dealt" from this infinitely large deck, there are still an infinite number of that card remaining in the deck. The following questions assume that we are talking about an infinitely large deck of digital cards containing no jokers. Indicate probabilities as percentages to 2 decimal places (e.g., .66666.. = 66.67%). 1. When dealing a card from this deck to each player, why are these random samples? 2. What is the size of the sample space for drawing a single card? 3. What is the probability that you are dealt a(n) even-numbered card

Each card in a standard deck of cards has a rank and a suit. The cards are ranked from 2 to 10, followed by the 3 face cards: Jack, Queen, King, and the highest ranked card is the Ace, for a total of 13 card ranks. There are four card suits (spades -, clubs hearts -, diamonds -). In total, the deck has 52 cards with a rank and a suit. A casino might use digital cards displayed on a screen, which allows the dealer to deal from a deck with an infinite number of cards. When a card, (e.g., Q♥) is "dealt" from this infinitely large deck, there are still an infinite number of that card remaining in the deck. The following questions assume that we are talking about an infinitely large deck of digital cards containing no jokers. Indicate probabilities as percentages to 2 decimal places (e.g., .66666.. = 66.67%). 1. When dealing a card from this deck to each player, why are these random samples? 2. What is the size of the sample space for drawing a single card? 3. What is the probability that you are dealt a(n) even-numbered card

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
See similar textbooks
icon
Related questions
Question
## Understanding Card Probabilities in a Deck ### Basic Information Each card in a standard deck has a rank and a suit. The ranks range from 2 to 10, followed by three face cards: Jack, Queen, King. The highest rank is the Ace, making 13 ranks in total. The four suits are: - **Spades (♠)** - **Clubs (♣)** - **Hearts (♥)** - **Diamonds (♦)** Altogether, the deck comprises 52 cards. In a casino context, digital screens may simulate infinitely large decks, with cards remaining constant in probability. ### Questions & Explanations 1. **Random Samples in Card Dealing** - When a card is dealt, it is considered a random sample due to the unpredictability and equal chance of any card being chosen from the infinite deck. 2. **Size of the Sample Space** - The sample space for drawing a single card is 52, representing all cards in the deck. 3. **Probability of Even-Numbered Cards** - Cards 2, 4, 6, 8, and 10 are even, giving a total of 20 even cards (5 per suit). The probability is \( \frac{20}{52} \times 100\% = 38.46\% \). 4. **Probability of a Club Face Card** - There are 3 face cards (Jack, Queen, King) in each suit. Thus, the probability is \( \frac{3}{52} \times 100\% = 5.77\% \). 5. **Blackjack Probability of Exceeding 21** - If dealt an 8 and a 9 (total 17), drawing any card over 4 will exceed 21. There are 32 cards with values that could push the total over 21 (7-10 and face cards from four suits). The probability is \( \frac{32}{52} \times 100\% = 61.54\% \). 6. **Probability of a Blackjack** - A Blackjack requires an Ace with a 10-point card (10, Jack, Queen, or King). There are 16 such cards of either spades or clubs. The probability is \( \frac{16}{52} \times 100\% = 30.77\% \).
Transcribed Image Text:## Understanding Card Probabilities in a Deck ### Basic Information Each card in a standard deck has a rank and a suit. The ranks range from 2 to 10, followed by three face cards: Jack, Queen, King. The highest rank is the Ace, making 13 ranks in total. The four suits are: - **Spades (♠)** - **Clubs (♣)** - **Hearts (♥)** - **Diamonds (♦)** Altogether, the deck comprises 52 cards. In a casino context, digital screens may simulate infinitely large decks, with cards remaining constant in probability. ### Questions & Explanations 1. **Random Samples in Card Dealing** - When a card is dealt, it is considered a random sample due to the unpredictability and equal chance of any card being chosen from the infinite deck. 2. **Size of the Sample Space** - The sample space for drawing a single card is 52, representing all cards in the deck. 3. **Probability of Even-Numbered Cards** - Cards 2, 4, 6, 8, and 10 are even, giving a total of 20 even cards (5 per suit). The probability is \( \frac{20}{52} \times 100\% = 38.46\% \). 4. **Probability of a Club Face Card** - There are 3 face cards (Jack, Queen, King) in each suit. Thus, the probability is \( \frac{3}{52} \times 100\% = 5.77\% \). 5. **Blackjack Probability of Exceeding 21** - If dealt an 8 and a 9 (total 17), drawing any card over 4 will exceed 21. There are 32 cards with values that could push the total over 21 (7-10 and face cards from four suits). The probability is \( \frac{32}{52} \times 100\% = 61.54\% \). 6. **Probability of a Blackjack** - A Blackjack requires an Ace with a 10-point card (10, Jack, Queen, or King). There are 16 such cards of either spades or clubs. The probability is \( \frac{16}{52} \times 100\% = 30.77\% \).
Expert Solution
steps

Step by step

Solved in 4 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability
A First Course in Probability
Probability
ISBN:
9780321794772
Author:
Sheldon Ross
Publisher:
PEARSON
SEE MORE TEXTBOOKS