Question

Five cards are drawn with replacement from a standard deck of 52 cards consisting of four suits of thirteen cards each. Calculate the probability that the five cards result in a flush (all five cards are of the same suit and round to the fourth decimal)

Answer 1

The first card it does not matter what the suit is. Any of the suits can be drawn initially, as long as the next four cards are of the same suit as the original card.
There are 13 cards in every suit of the deck, so after the first card is drawn, there are only 12 cards in the suit. Then after the second card is drawn there is 11 cards left in the suit. Then 10 cards left for the fouth drawn and 9 cards left for the final(5th) drawn.
Also there is one less card total in the deck each time.
P(flush)=P(2nd card drawn from the same suit)*P(3rd card drawn from the same suit)*P(4th card drawn from the same suit)*P(5th card drawn from the same suit)
  $=\frac{12}{51}*\frac{11}{50}*\frac{10}{49}*\frac{9}{48}$
  $=\frac{11880}{5997600}$
  $=0.0019$

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