Assume that you are playing poker with a standard 52-card deck of playing cards
ID: 3059550 • Letter: A
Question
Assume that you are playing poker with a standard 52-card deck of playing cards and you are dealt 5 cards. Calculate the probability that you were dealt the following hands. Use any method you wish to perform the calculations (permutations, combinations, conditional probability, brute force counting, etc.). Note that for a test, I will accept answers that are left using combinations, but for this assignment please find the numerical values of the probabilities, to put everything in context.
a) only one pair (ex: AA58K)
b) two pairs (ex: AAKK4)
c) three of a kind (ex: AAA47)
d) straight (5 cards in sequence, using any suit – exclude the cases when all 5 cards are of the same suit) (ex: 45678)
e) flush (5 cards of the same suit – exclude the cases when the cards are in sequence)
f) full house (three of a kind and a pair) (ex: AAAKK)
g) four of a kind (ex: AAAAK)
h) straight flush (5 cards in sequence of the same suit)
Explanation / Answer
Assume that you are playing poker with a standard 52-card deck of playing cards and you are dealt 5 cards. Calculate the probability that you were dealt the following hands. Use any method you wish to perform the calculations (permutations, combinations, conditional probability, brute force counting, etc.). Note that for a test, I will accept answers that are left using combinations, but for this assignment please find the numerical values of the probabilities, to put everything in context.
a) only one pair (ex: AA58K)
b) two pairs (ex: AAKK4)
c) three of a kind (ex: AAA47)
d) straight (5 cards in sequence, using any suit – exclude the cases when all 5 cards are of the same suit) (ex: 45678)
e) flush (5 cards of the same suit – exclude the cases when the cards are in sequence)
f) full house (three of a kind and a pair) (ex: AAAKK)
g) four of a kind (ex: AAAAK)
h) straight flush (5 cards in sequence of the same suit)