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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= α/C(52,5), where α=_______
(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= β/C(52,5), where β=_______
(c) What is the probability that the hand is a straight flush? Answer= γ/C(52,5), where γ=________

Answer :

Answer:

Step-by-step explanation:

a) The probability that the hand contains exactly one ace

No of ways of selecting one ace and four non ace would be

=[tex]4C1 (48C4)\\\\= 778320[/tex]

i.e. α=778320

b) the probability that the hand is a flush

No of ways of getting a flush is either all 5 hearts or clubs of spades or dice

= [tex]4(13C5) = 5148[/tex]

ie. β=5148

c)  the probability that the hand is a straight flush

In each of the suit to get a straight flush we must have either A,2,3,4,5 or 2,3,4,5,6, or .... or 9,10, J, q, K

So total no of ways = [tex]=9(13C5) 4\\= 46332[/tex]

γ=46332

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