probability

OSDG

Hey can anyone help me with this question???

A poker hand is obtained by drawing 5 cards at random without replacement from a pack of 52, Find the probabilitly of getting 4 of a kind?


THanks so much!

AdMMM

There are 2,598,960 possible hands in poker. There are 624 combinations of cards that make up four of a kind out of 2,598,960 possible hands. 624 is obtained by multiplying 13 x 48, where 13 is the amount of different cards that can make up a four of a kind (A,2,3,4,5,6,7,8,9,10,J,Q,K) and 48 is the number of other cards available after 4 of a kind take up the first four positions of a 5 card poker hand.

2,598,960 / 624 = 4165

Therefore you have a one in 4165 chance of getting a four in a kind.

Figures obtained from: http://www.indepthinfo.com/probability-poker/four-of-a-kind.shtml

BobbyOLeary

Here's a bit of an easier way to do it, you can use this approach to work out similar problems.

52 cards in a deck (4 each of A2345678910JQK)

You want 4 cards of the same value. The first card you pick doesn't matter as it can be anyone at all. Chances of drawing card: 52/52

The next card you want has to be the same as the first but this time there's one less card and only three remaining cards of the same value so your probability is: 3/51

Much the same for the next card, it has to be the same but there's only two left in the deck now so probability is: 2/50

Same principle for the 4th card, probability 1/49

Since you're only looking for 4 of a kind the last card doesn't matter, it can be anything, so the probability is 48/48

To get the probability of these all happening at once, i.e. in one hand, multiply them together:

52/52 * 3/51 * 2/50 * 1/49 * 48/48 = 6/Something large( I don't have a calculator handy)

Hope that helps, if you want a tougher one try and work out the probability of getting a full house (Three of a kind + a pair)

Bob

OSDG

thanks guys that cleared it up!

Steve01

I'm in the middle of 6th year now and haven't done probability since TY! Though we have most of the course covered at this stage so I'm not doing too bad

1huge1

I could of sword i heard that they wouldnt give a question like this because its general knowledge (knowing about cards) and not everyone knows it (as hard to believe as that is)

i dropped down to ordinary level maths 2 weeks ago
so easy

oRlyYaRly

1huge1 wrote:

I could of sword i heard that they wouldnt give a question like this because its general knowledge (knowing about cards) and not everyone knows it (as hard to believe as that is)

Everybody who studies probability will though because all the text books use cards in their questions.

JC 2K3

1huge1 wrote:

I could of sword i heard that they wouldnt give a question like this because its general knowledge (knowing about cards) and not everyone knows it (as hard to believe as that is)

All they have to say is:
-A deck of cards has 52 cards
-Half are black and half are red
-A quarter are diamonds, a quarter are hearts, a quarter are clubs and a quarter are spades.
-Every suit of diamonds, hearts, clubs and spades each contain an Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen and King card.