poker straight probability
A five-card poker hand is dealt at random from a standard 52-card deck.?
Note the total number of possible hands is C(52,5)=2,598,960.
Find the probabilities of the following scenarios:
(a) What is the probability that the hand contains exactly one ace?
Answer= a/ C(52,5), where a=
(b) What is the probability that the hand is a flush? (That is all the cards are of the same suit: hearts, clubs, spades or diamonds.)
Answer= b/ C(52,5), where b=
(c) What is the probability that the hand is a straight flush?
Answer= c/ C(52,5), where c=
a)
4C1*48C4 = 778,320 = a
b)
flush:
13C5*4 = 5,148
this includes straight flushes and royal flushes
straight flush:
from A-5 to 9-K -> 9
total four suits = 9*4 = 36
royal flush:
from 10-A -> 1
total four suits = 1*4 = 4
flush -> 5,148 – 36 – 4 = 5,108 = b
c)
from b),
straight flush -> 36 = c
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