Part A Poker Hands: In this activity, we will apply some of the
various counting techniques...
Part A Poker Hands: In this activity, we will apply some of the
various counting techniques that we have studied including the
product and sum rules, the principle of inclusion-exclusion,
permutations, and combinations. Our application will be counting
the number of ways to be dealt various hands in poker, and
analyzing the results.
First, if you are not familiar with poker the following is some
basic information. These are the possible 5-card
hands:
Royal Flush (A,K,Q,J,10 of the same suit);...
Suppose you are playing a game of five-card poker where you are
dealt a hand of...
Suppose you are playing a game of five-card poker where you are
dealt a hand of 5 cards from a standard deck of 52 playing cards.
Each card has one of 13 values, 2,3,…,10,J,Q,K,A2,3,…,10,J,Q,K,A,
and one of 4 suits, ♡,♢,♠,♣♡,♢,♠,♣
A hand called a royal flush consists of cards of
the values 10,J,Q,K,A10,J,Q,K,A, all from the same suit. For
instance, a royal flush with hearts would be
10♡,J♡,Q♡,K♡,A♡10♡,J♡,Q♡,K♡,A♡.
Now, actually getting a royal flush in poker is incredibly rare (in...
Five cards are selected from a 52-card deck for a poker hand. a.
How many simple...
Five cards are selected from a 52-card deck for a poker hand. a.
How many simple events are in the sample space? b. A royal flush is
a hand that contains the A, K, Q, J, and 10, all in the same suit.
How many ways are there to get a royal flush? c. What is the
probability of being dealt a royal flush? Please, please, please
explain and not just give the answer or formula.
5. In poker, a “flush” is a five-card hand where all five cards
have the same...
5. In poker, a “flush” is a five-card hand where all five cards
have the same suit. A hand has “three of a kind” when any three
cards have the same rank. “Four of a kind” is defined analogously.
A flush beats a three of a kind, but is beaten by four of a kind.
Demonstrate that this ranking of hands corresponds to how unlikely
each hand type is to occur when drawing five cards at random (Hint:
just count...
5 cards are randomly selected from a standard deck of 52
cards to form a poker...
5 cards are randomly selected from a standard deck of 52
cards to form a poker hand. Determine the probability of being
dealt a straight flush (five cards in sequence in the same suit but
not a royal flush. Note: A royal flush is 10, Jack, Queen, King,
Ace all in the same suit. Note: Aces can be high or
low).
Probabilities with a deck of cards. There are 52 cards in a
standard deck of cards....
Probabilities with a deck of cards. There are 52 cards in a
standard deck of cards. There are 4 suits (Clubs, Hearts, Diamonds,
and Spades) and there are 13 cards in each suit. Clubs/Spades are
black, Hearts/Diamonds are red. There are 12 face cards. Face cards
are those with a Jack (J), King (K), or Queen (Q) on them. For this
question, we will consider the Ace (A) card to be a number card
(i.e., number 1). Then for each...
Determine the poker odds of drawing the following hand from a
standard card deck. (4 suits,...
Determine the poker odds of drawing the following hand from a
standard card deck. (4 suits, 13 ranks in each suit.) What are the
odds of drawing a royal flush (AKQJ10 all of the same suit)?
Drawing cards is WITHOUT replacement. (NOTE: If necessary, lay out
52 cards on a table and do a dry run before computing the
probabilities!) In order to get a royal flush in spades, you must
pick the following 5 cards:
What is the probability...
A sequence is a hand consisting of five consecutive cards of any
suit(e.g., 5♥−6♥−7♠−8♦−9♣). An ace...
A sequence is a hand consisting of five consecutive cards of any
suit(e.g., 5♥−6♥−7♠−8♦−9♣). An ace may be either high (as
in10-J-Q-K-A, or low, as in A-2-3-4-5, but can’t “wrap around”
(Q-K-A-2-3 is not a valid sequence). How many different sequence
hands are possible?
(b) How many hands consist of cards that are all of the same
suit?(
c) A straight flush has both of these properties – a sequence
all of the same suit. How many different straight flushes...