We are creating a new card game with a new deck. Unlikethe normal deck that has 13 ranks (Ace through King) and 4 Suits(hearts, diamonds, spades, and clubs), our deck will be made up ofthe following.
Each card will have:
i) One rank from 1 to 16.
ii) One of 5 different suits.
Hence, there are 80 cards in the deck with 16 ranks for each of the5 different suits, and none of the cards will be face cards! So, acard rank 11 would just have an 11 on it. Hence, there is nodiscussion of \"royal\" anything since there won't be any cards thatare \"royalty\" like King or Queen, and no face cards!
The game is played by dealing each player 5 cards from the deck.Our goal is to determine which hands would beat other hands usingprobability. Obviously the hands that are harder to get (i.e. aremore rare) should beat hands that are easier to get.
e) How many different ways are there to get exactly 3 ofa kind (i.e. 3 cards with the same rank)?
The number of ways of getting exactly 3 of a kind is
DO NOT USE ANY COMMAS
What is the probability of being dealt exactly 3 of akind?
Round your answer to 7 decimal places.
f) How many different ways are there to get exactly 4 ofa kind (i.e. 4 cards with the same rank)?
The number of ways of getting exactly 4 of a kind is
DO NOT USE ANY COMMAS
What is the probability of being dealt exactly 4 of akind?
Round your answer to 7 decimal places.
g) How many different ways are there to get a full house(i.e. 3 of a kind and a pair, but not all 5 cards the samerank)?
The number of ways of getting a full house is
DO NOT USE ANY COMMAS
What is the probability of being dealt a fullhouse?
Round your answer to 7 decimal places.
h) How many different ways are there to get a straightflush (cards go in consecutive order like 4, 5, 6, 7, 8 and allhave the same suit. Also, we are assuming there is no wrapping, soyou cannot have the ranks be 14, 15, 16, 1, 2)?
The number of ways of getting a straight flush is
DO NOT USE ANY COMMAS
What is the probability of being dealt a straightflush?
Round your answer to 7 decimal places.
i) How many different ways are there to get a flush (allcards have the same suit, but they don't form astraight)?
Hint: Find all flush hands and then just subtract the number ofstraight flushes from your calculation above.
The number of ways of getting a flush that is not astraight flush is
DO NOT USE ANY COMMAS
What is the probability of being dealt a flush that is nota straight flush?
Round your answer to 7 decimal places.
j) How many different ways are there to get a straight thatis not a straight flush (again, a straight flush has cards that goin consecutive order like 4, 5, 6, 7, 8 and all have the same suit.Also, we are assuming there is no wrapping, so you cannot have theranks be 14, 15, 16, 1, 2)?
Hint: Find all possible straights and then just subtract thenumber of straight flushes from your calculation above.
The number of ways of getting a straight that is not astraight flush is
DO NOT USE ANY COMMAS
What is the probability of being dealt a straight that isnot a straight flush?
Round your answer to 7 decimal places.
