Probability Q. (1 Viewer)

[Trev]

i forget the question but heres the gist of it:
you have a poker hand of FIVE cards, from a deck of cards (52 cards), what is the chance of having ONE pair in your hand?
EH? ive written down a few things in relation to the question, but i dont really kno how to go about figuring it out.......... can any1 figure it out?
thanx

 

[QuaCk]

1 x 3/51 x 48/50 x 47/49 x 46/48

that's my guess :S
i'd say it's wrong though
probability fucks me over.

 

[QuaCk]

i THINK only

 

[Trev]

only one pair! hav fun

 

[Xayma]

Well lets see the cases we must consider:

Only one pair, now I take this to mean that having 3 of a kind and 4 of a kind is also out (since you would have the pair, but it might not).

Which means you are looking for:

1*3/51*46/48*43/47*40/46.

Since of the remaining 3 cards, one cant be the original nor can it be of the same value of any card already drawn.

 

[Trev]

going through Xayma's answer, it seems pretty right to me, ill try find the answer

 

[Dreamerish*~]

yes, xayma IS right.
i'm going to delete my post

 

[Trev]

haha u could just change it so its the right answer ey?

 

[QuaCk]

i'll reiterate:
i hate probability......

 

[Trev]

wait, the answer from the book isnt the same as what you got Xayma!
its: (4C2*13*12C3*43)/(52C5)
so........eh?

 

[Xayma]

Oh yeah thats because I had that the first two must be a pair. Rather than any two.

⁴C₂ is that it can be any two out of the 4 types of cards.

13 is that it can be any pair

¹²C₃ in that you must have 3 cards from 12 others and they can occur in any order. (Ie say you have a pair of aces, then you can only have one of 2,3,4,5 etc

43 has to do with something Ill figure it out soon

⁵²C₅ how many total combinations are possible.

 

[Trev]

kool thanx, have u figured out why it is multiplied by 43 yet?

 

[illin]

Yeah we went through this one in class
3u Cambridge right?
well it goes 52/52*3/51*48/50*44/49*40/48*52C5

choose any 1 card, choose the remaining 3 types of the same card, choose the rest except for the other 2 of the same card, repeat, repeat, unorder the cards

the other ones are a lot harder
ie. two pair, three of a kind, etc..
except royal flush is easiest