Problem 3. A standard deck of cards contains 52 cards: 13 Ranks: A,2,3,4,5,6,7,8,9,10,J,Q,K 4 Suits: Clubs,...

Problem 3. A standard deck of cards contains 52 cards:

13 Ranks: A,2,3,4,5,6,7,8,9,10,J,Q,K
4 Suits: Clubs, Diamonds, Hearts, Spades

Suppose you draw a hand of 5 cards from the deck. Consider the following possible hands of cards. For each part, explain how you derive your solutions.

3(a) How many different hands of 5 cards exist?

3(b) How many ways can you draw a single pair? A single pair means that there are exactly two cards with the same rank (no additional pairs and no 3 of a kind, etc.).

3(c) How many ways can you draw 4 of a kind? (4 cards of the same rank)

3(d) How many ways can you draw a full house? A full house is a pair of one rank and three cards of another rank.

3(e) How many ways can you draw a straight? A straight is 5 consecutive ranks. The Ace (A) can either go before 2 or after K.
E.g., A,2,3,4,5 and 10,J,Q,K,A are both valid, as are 4,5,6,7,8 and 7,8,9,10,J etc.

Note: if you were to divide the number of hands of a particular type by the total number of 5 card hands, you would achieve the probability (odds) of randomly drawing a hand of that type.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

consider a standard deck of playing cards... 52 cards, 4 suits of 13 cards each, 3...

consider a standard deck of playing cards... 52 cards, 4 suits of 13 cards each, 3 cards of each suit are face cards, 2 suits are black (clubs and spades) and 2 are red (hearts and diamond) a) Let event A be drawing a random card that is a diamond. What is a trial for this scenario? What is the sample space? Is A a simple event? What is P(A)? What is A¯, the complement of A? What is P(A¯)?...

In a standard deck of 52 cards, there are four suits (clubs, hearts, diamonds and spades)...

In a standard deck of 52 cards, there are four suits (clubs, hearts, diamonds and spades) and 13 cards of each suit. What is the probability of randomly selecting two cards, which turn out to be the same suit? (Answer to 2 digits after the decimal point.)

Hyram has a standard deck of 52 playing cards. The deck contains 4 suits (hearts, diamonds,...

Hyram has a standard deck of 52 playing cards. The deck contains 4 suits (hearts, diamonds, clubs, and spades), and each suit contains 13 cards labeled 2 through 10, as well as jack, queen, king, and ace. Four friends are trying to determine some probabilities related to randomly drawing a single card from the deck. Consider the following events, and then answer the question. A: drawing a diamond B: drawing a queen Which friend provided the correct analysis? Samantha says...

A deck of cards contain 52 cards consisting of 4 suits (Clubs, Diamonds, Hearts and Spades)...

A deck of cards contain 52 cards consisting of 4 suits (Clubs, Diamonds, Hearts and Spades) and each suit has 13 cards. Cards are drawn one at a time at random with replacement. (a) What is the expected time to get a card of Hearts? (b) What is the expected time to get 4 cards with different suits? Hint: The waiting times between getting i cards of different suits and i + 1 cards of different suits are independent, where...

In a standard deck of cards, there are 4 suits (Clubs, Hearts, Diamonds, and Spades) and...

In a standard deck of cards, there are 4 suits (Clubs, Hearts, Diamonds, and Spades) and 13 ranks of each suit (2 through 10, Jack, Queen, King, Ace). The diamonds and hearts are red, spades and clubs are black. Imagine drawing cards (without replacement) from a shuffled deck, so that any card in the deck is equally likely to be drawn. What is the probability that (a) If you draw 5 cards, no cards in your hand are red? (b)...

In a standard deck of cards, there are 4 suits (Clubs, Hearts, Diamonds, and Spades) and...

A standard deck of cards has 52 cards, four each of 2,3,4,5,6,7,8,9,10,J,Q,K,A. In blackjack, a player...

A standard deck of cards has 52 cards, four each of 2,3,4,5,6,7,8,9,10,J,Q,K,A. In blackjack, a player gets two cards and adds their values. Cards count as their usual numbers, except Aces are 11 (or 1), while K, Q, J are all 10. “Blackjack” means getting an Ace and a value ten card. What is probability of getting a blackjack? What is probability of getting 19? (The probability that the sum of your cards is 19, using Ace as 11) Use...

A standard 52-card deck of French playing cards consists of four suits: hearts, spades, clubs, and...

A standard 52-card deck of French playing cards consists of four suits: hearts, spades, clubs, and diamonds. There are 13 cards of each suit; each suit has cards of rank 2 through 10, along with an ace, king, queen, and jack. Typically, hearts and diamonds are the red suits, while spades and clubs are the black suits. Four cards are drawn from the deck, one at a time, without replacement. a) The second card drawn is from a red suit....

2.Deck of cards(52 total cards; 13 denominations in each of 4 suits). Select a single card...

2.Deck of cards(52 total cards; 13 denominations in each of 4 suits). Select a single card at random from a deck of cards: a.Whatis the probability of selecting the king of hearts? b.What is the probability of selecting a king? c.What is the probability of selecting a heart? d.What is the probability of selecting a king or a heart?

Assume that a standard deck of 52 playing cards is randomly shuffled (13 cards of 4...

Assume that a standard deck of 52 playing cards is randomly shuffled (13 cards of 4 types of suits - clubs, diamonds, hearts, and spades). If Alex draws a card from it 4 times with replacement, how many different combinations of suits can he get? (Suppose we further assume that the order doesn't matter: (clubs, diamonds, hearts, hearts) is equal to (hearts, clubs, diamonds, hearts). However, (clubs, diamonds, hearts, hearts) is different with (hearts, clubs, clubs, hearts).)

Subjects