Here is a table showing all 52 cards in a standard deck. Face cards Color Sult Ace Two Three Four Five Six Seven Eight Nine Ten Jack Queen King Hearts A 2♥ 3 4 5 6 7♥ 9v 10v J Q♥ Red KV Red Diamonds A 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ J+ Q+ Spades Ae 24 34 44 54 6+ 7+ 94 104 Je Black K+ Clubs A 24 34 4+ 54 6+ 74 84 94 104 J+ Q4 Black A card is drawn at random from a standard deck. That card is not put back in the deck, and a second card is drawn at random from the remaining cards in the deck. Neither of the cards drawn so far are put back in the deck, and a third card is drawn at random from the remaining cards in the deck. What is the probability that the first card drawn is a diamond, the second card drawn is a diamond, and the third card drawn is a club? Do not round your intermediate computations. Round your final answer to four decimal places.
Here is a table showing all 52 cards in a standard deck. Face cards Color Sult Ace Two Three Four Five Six Seven Eight Nine Ten Jack Queen King Hearts A 2♥ 3 4 5 6 7♥ 9v 10v J Q♥ Red KV Red Diamonds A 2+ 3+ 4+ 5+ 6+ 7+ 8+ 9+ 10+ J+ Q+ Spades Ae 24 34 44 54 6+ 7+ 94 104 Je Black K+ Clubs A 24 34 4+ 54 6+ 74 84 94 104 J+ Q4 Black A card is drawn at random from a standard deck. That card is not put back in the deck, and a second card is drawn at random from the remaining cards in the deck. Neither of the cards drawn so far are put back in the deck, and a third card is drawn at random from the remaining cards in the deck. What is the probability that the first card drawn is a diamond, the second card drawn is a diamond, and the third card drawn is a club? Do not round your intermediate computations. Round your final answer to four decimal places.
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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Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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Transcribed Image Text:### Understanding Probability with Standard Deck Cards
#### Introduction to Standard Deck Cards:
A standard deck of playing cards consists of 52 cards divided into four suits: Hearts, Diamonds, Spades, and Clubs. Each suit comprises 13 cards: Ace, Two, Three, Four, Five, Six, Seven, Eight, Nine, Ten, Jack, Queen, and King.
#### Table of Standard Deck Cards:
| Color | Suit | Ace | Two | Three | Four | Five | Six | Seven | Eight | Nine | Ten | Face cards |
|-------|----------|-----|-----|-------|------|------|-----|-------|-------|------|-----|--------------------------|
| Red | Hearts | A♥ | 2♥ | 3♥ | 4♥ | 5♥ | 6♥ | 7♥ | 8♥ | 9♥ | 10♥ | J♥ Q♥ K♥ |
| Red | Diamonds | A♦ | 2♦ | 3♦ | 4♦ | 5♦ | 6♦ | 7♦ | 8♦ | 9♦ | 10♦ | J♦ Q♦ K♦ |
| Black | Spades | A♠ | 2♠ | 3♠ | 4♠ | 5♠ | 6♠ | 7♠ | 8♠ | 9♠ | 10♠ | J♠ Q♠ K♠ |
| Black | Clubs | A♣ | 2♣ | 3♣ | 4♣ | 5♣ | 6♣ | 7♣ | 8♣ | 9♣ | 10♣ | J♣ Q♣ K♣ |
#### Problem Statement:
A card is drawn at random from a standard deck. That card is not put back in the deck, and a second card is drawn at random from the remaining cards in the deck. Neither of the cards drawn so far are put back in the deck, and a third card is drawn at random from the remaining cards in the deck.
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