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probability that both cards have rank no higher than 10, and at least one of the cards is red?

probability that both cards have rank no higher than 10, and at least one of the cards is red?

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...
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This problem will refer to a standard deck of cards. Each card in such a deck has
a rank and a suit. The 13 ranks, ordered from lowest to highest, are 2, 3, 4, 5, 6, 7, 8, 9, 10,
jack, queen, king, and ace. The 4 suits are clubs (♣), diamonds (♢), hearts (♡), and spades (♠).
Cards with clubs or spades are black, while cards with diamonds or hearts are red. The deck
has exactly one card for each rank–suit pair: 4 of diamonds, queen of spades, etc., for a total of
13 · 4 = 52 cards. Take a look at the screenshot please!

**Probability Problem: Selecting Cards from a Deck** Suppose you select a card uniformly at random from a standard deck, and then without putting it back, you select a second card uniformly at random from the remaining cards. What is the probability that both cards have rank no higher than 10, and at least one of the cards is red? **Understanding the Problem:** 1. **Deck Composition**: - A standard deck has 52 cards. - Each suit (hearts, diamonds, clubs, spades) has 13 cards each. 2. **Cards of Rank 10 or Lower**: - Ranks 1 (Ace) through 10 are valid (4 suits per rank). - Total cards with rank 10 or lower = 10 ranks × 4 suits = 40 cards. 3. **Red Cards**: - Red suits = Hearts and Diamonds. - Total red cards = 2 suits × 13 cards per suit = 26 cards. 4. **Red Cards with Rank 10 or Lower**: - 10 ranks × 2 red suits = 20 red cards. 5. **Calculating Probability**: - Look for combinations where both drawn cards are of rank 10 or lower and at least one is red. This problem involves computing probabilities considering the constraints of ranks and colors in a deck of cards.
Transcribed Image Text:**Probability Problem: Selecting Cards from a Deck** Suppose you select a card uniformly at random from a standard deck, and then without putting it back, you select a second card uniformly at random from the remaining cards. What is the probability that both cards have rank no higher than 10, and at least one of the cards is red? **Understanding the Problem:** 1. **Deck Composition**: - A standard deck has 52 cards. - Each suit (hearts, diamonds, clubs, spades) has 13 cards each. 2. **Cards of Rank 10 or Lower**: - Ranks 1 (Ace) through 10 are valid (4 suits per rank). - Total cards with rank 10 or lower = 10 ranks × 4 suits = 40 cards. 3. **Red Cards**: - Red suits = Hearts and Diamonds. - Total red cards = 2 suits × 13 cards per suit = 26 cards. 4. **Red Cards with Rank 10 or Lower**: - 10 ranks × 2 red suits = 20 red cards. 5. **Calculating Probability**: - Look for combinations where both drawn cards are of rank 10 or lower and at least one is red. This problem involves computing probabilities considering the constraints of ranks and colors in a deck of cards.
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