Question
In: Advanced Math
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
Colby Messinger answered 2 years agoRelated 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¯)?...
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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...
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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?
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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)...
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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 2 cards, you get both • an Ace,
• a...
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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
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Use...
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1. (15pts)
A standard 52-card deck consists of 13 cards from each of 4 suits
(spades, hearts, diamonds, clubs). What is the probability that a
5-card poker hand drawn from a standard 52-card deck has (please
give necessary explanation as the solution)
(a) (5pts) 2 clubs, 1 hearts and 2 diamonds?
(b) (5pts) 1 ace and 2 face cards (face cards refer to king, queen,
or jack)?
(c) (5pts) at least one ace?
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ace, king, queen, and jack. Typically, hearts and diamonds are the
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Four cards are drawn from the deck, one at a time, without
replacement.
a) The second card drawn is from a red suit....
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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?
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