Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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According to the question in the image, what is the correct answer to "What is the probability of this event?"?

**Title: Understanding Probability with a Deck of Cards**

An ordinary deck of cards contains 52 cards divided into four suits. The **red suits** are diamonds (♦) and hearts (♥), and the **black suits** are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards.

Imagine choosing a card at random from a thoroughly mixed deck. Consider the event that the chosen card is **black** and has an **even number** on it. Which of the following expresses this event as a set?

Options:
- {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣} ✔️
- {2♠, 4♠, 6♠, 8♠, 2♣, 4♣, 6♣, 8♣}
- {2♥, 4♥, 6♥, 8♥, 10♥, 2♦, 4♦, 6♦, 8♦, 10♦}
- {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣, 2♥, 4♥, 6♥, 8♥, 10♥}

The correct answer is the first option: {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣}.

**Question: What is the probability of this event?**

The probability is \( \frac{10}{52} \).

Explanation: 
- There are 10 black cards with even numbers (five from spades and five from clubs out of the 52 total cards in the deck).

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Transcribed Image Text:**Title: Understanding Probability with a Deck of Cards** An ordinary deck of cards contains 52 cards divided into four suits. The **red suits** are diamonds (♦) and hearts (♥), and the **black suits** are clubs (♣) and spades (♠). Each suit contains 13 cards of the following denominations: 2, 3, 4, 5, 6, 7, 8, 9, 10, J (jack), Q (queen), K (king), and A (ace). The cards J, Q, and K are called face cards. Imagine choosing a card at random from a thoroughly mixed deck. Consider the event that the chosen card is **black** and has an **even number** on it. Which of the following expresses this event as a set? Options: - {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣} ✔️ - {2♠, 4♠, 6♠, 8♠, 2♣, 4♣, 6♣, 8♣} - {2♥, 4♥, 6♥, 8♥, 10♥, 2♦, 4♦, 6♦, 8♦, 10♦} - {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣, 2♥, 4♥, 6♥, 8♥, 10♥} The correct answer is the first option: {2♠, 4♠, 6♠, 8♠, 10♠, 2♣, 4♣, 6♣, 8♣, 10♣}. **Question: What is the probability of this event?** The probability is \( \frac{10}{52} \). Explanation: - There are 10 black cards with even numbers (five from spades and five from clubs out of the 52 total cards in the deck). This exercise enhances
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