SOLUTION: A flush can occur if a player receives five clubs or five diamonds or five hearts or five spades. Compute P(five clubs or five diamonds or five hearts or five spades). Note t
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Question 1155350: A flush can occur if a player receives five clubs or five diamonds or five hearts or five spades. Compute P(five clubs or five diamonds or five hearts or five spades). Note that the events are mutually exclusive.
P(five clubs or five diamonds or five hearts or five spades)equals Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website! Let's look at spades, as an example:
P(1st card is a spade) = 13/52 = 1/4
P(2nd is a spade) = 12/51
P(3rd is a spade) = 11/50
P(4th is a spade) = 10/49
P(5th is a spade) = 9/48
P(all 5 cards are spades) = (13/52)(12/51)(11/50)(10/49)(9/48) = 154440/311875200
Since we are looking for any flush, just multiply the above by 4 (essentially, the first card is a freebie, that's why I simplified the first fraction to 1/4):
(12/51)(11/50)(10/49)(9/48) = 11880/5997600 = or about 1 in 505 hands.
This answers the question as asked; however, this INCLUDES straight-flushes (where the rank of the cards are in consecutive order such as 5-6-7-8-9 of hearts). If you want an answer that does not include traight-flushes in the count of ordinary flushes then note there are 40 straight-flushes in 52C5 poker hands (works out to a probability of 0.00001539). Subtracting this quantity from the first highlighted answer gives P(true flush) = , or about 1 in 509 hands.
