Question

A 5-card poker hand is dealt from a well shuffled regular 52-card playing card deck. Find the probability that the hand is a Flush (5 nonconsecutive cards each of the same suit).

Answer 1

Explanation:

There are 4 suits (clubs, diamonds, hearts, spades) Any one of them could contain the flush.

So the first part of your answer is

4 Then you must choose 5 cards from 13 or 13 C 5 - 9 see below.

Finally you must choose the total number of possible 5 card hands from 52 cards.

The remaining question is, how do you get rid of all the straights (cards that are in order?)

I think that is done by subtracting

1 number of straights that are royal straights

1 number of straights starting with the queen

1 number of straights starting with the jack

1 number of straights starting with the 10

1 number of straights starting with the 9

1 number of straights starting with the 8

1 number of straights starting with the 7

1 number of straights starting with the6

1 number of straights starting with the 5

Total 9

4* 13 c 5 - 9 = 5139

52 C 5 = 2598960

Probabiity Flush = 5139/2598960 = 0.00197