# Thread: The Probability of a Flush

1. ## The Probability of a Flush

Hiya Im back for some more assistance....

Q:

THE PROBABILITY OF A FLUSH A poker player holds a flush when all 5 cards in the hand belong to the same suit. We will find the probability of a flush when 5 cards are dealt. Remember that a deck contains 52 cards, 13 of each suit, and that when the deck is well shuffled, each card dealt is equally likely to be any of those that remain in the deck.

A) We will concentrate on spades. What is the probability that the first card dealt is a spade? What is the conditional probability that the second card is a spade, given that the first is a spade? Continue to count the remaining cards to find the conditional probabilities of a spade on the third, the fourth, and the fifth card, given in each case that all previous cards are spades.

I answered this one, no problem.... 0.25, 0.24, 0.22, 0.20, 0.19.

B) The probability of being dealt 5 spades is the product of the five probabilities you have found. Why? What is this probability?

I found out the probability of this - which is 0.0005016.9 - but why do we multiply to get this answer?

C) The probability of being dealt 5 hearts or 5 diamonds or 5 clubs is the same as the probability of being dealt 5 spades. What is the probability of being dealt a flush?

Do I multiply the probability of getting dealt the 5 spades by 4 because there are 4 suits to possibly get a flush with?

0.0005016.9*4=0.0020064

?

Thanks so much in advance.... more questions to come

2. B) because all of the individual events need to happen:

C) yes, or figure out the total number of possible flushes, and divide that by the total number of 5-card hands
=(52*12*11*10*9)/(52*51*50*49*48)

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