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 jrcsgtpeppers 01-21-2013 03:47 AM

help me with some probability

40 cards
8 red 8 blue 8 green 8 yellow 8 purple

i get to draw 6 cards and keep them all in my hand

what are the odds of drawing AT LEAST 1 red?
odds of drawing at least 1 red and 1 blue
odds of drawing at least 1 red 1 blue and 1 green

thats about as much as i need to know.

thanks if anyone shows me how its done. stats are harder thani thought.

 JustRooster 01-21-2013 03:51 AM

I'd say your odds are pretty good.

 jrcsgtpeppers 01-21-2013 03:54 AM

id like to think that too, but im sitting here thinking, whats the best way to beat all these spoiled rich kids in yugioh after their parents buy them boxes of the new pack series that just came out, and i thought, lets use math! then i remembered i never took stats :sad:

 JimDawson 01-21-2013 04:02 AM

Well, I didn't take this in school but...

8 is one fifth of 40. Since you're finding the odds of two types of cards with the same odds, I think you would figure out what one fifth of one fifth is, making it 1/25. Then you multipy it by six because that's how many times you're drawing cards.

Pretty sure your odds of getting at least one red and one blue are six out of twenty five, or 24%.

The second one would be 6/125, or 4.88%. Did the percentage in my head, and it's wrong. It's actually 4.8%. Damn, I've done more difficult things...

 Avedas 01-21-2013 04:03 AM

are you drawing with replacement or no? makes sort of a big difference. if yes, use permutations. if no, use combinations :)

 willT08 01-21-2013 04:03 AM

No chance mate.

 jrcsgtpeppers 01-21-2013 04:07 AM

Quote:
 Originally Posted by Avedas are you drawing with replacement or no? makes sort of a big difference. if yes, use permutations. if no, use combinations :)

no, i pick up 6 cards and keep them all in my hand, no replacement. how do i use combinations? is the above sir correct though?

 jrcsgtpeppers 01-21-2013 04:10 AM

Quote:
 Originally Posted by JimDawson Well, I didn't take this in school but... 8 is one fifth of 40. Since you're finding the odds of two types of cards with the same odds, I think you would figure out what one fifth of one fifth is, making it 1/25. Then you multipy it by six because that's how many times you're drawing cards. Pretty sure your odds of getting at least one red and one blue are six out of twenty five, or 24%. The second one would be 6/125, or 4.88%. Did the percentage in my head, and it's wrong. It's actually 4.8%. Damn, I've done more difficult things...

it cant be though... because i draw one of each very often. it would be hard to imagine having 5 sets of 8 cards and shuffling them then drawing 6 and not getting a card from 3/5 that i want. the other 2/5 is filler.

 JimDawson 01-21-2013 04:13 AM

Quote:
 Originally Posted by jrcsgtpeppers it cant be though... because i draw one of each very often. it would be hard to imagine having 5 sets of 8 cards and shuffling them then drawing 6 and not getting at least 3 different ones....

Yeah, I think the number of varieties comes into play here somehow... something seems a bit screwy to me too. This intrigues me, so I'll stick around and try some more things.

 jrcsgtpeppers 01-21-2013 04:18 AM

i feel silly putting this much thought into a childrens card game but you guys have no idea how competitive yugioh gets. to make the question easier:

40 cards
8 red 8 blue 8 green 8 yellow 8 purple

i get to draw 6 cards and keep them all in my hand

what are the odds of drawing AT LEAST 1 red?
odds of drawing at least 1 red and 1 blue
odds of drawing at least 1 red 1 blue and 1 green

thats about as much as i need to know.

 JimDawson 01-21-2013 04:31 AM

On each individual draw, for the first question, you would have a clear 1/5 chance of getting a red card. The hard part is that you have six draws- I know that it doesn't make sense to have your odds go above 100% in this kind of math, so 120% (6/5) is definitely wrong. I suspect there's some kind of calculus for this, and the odds are in the >80% range. I'm going to try messing with the fractions some more to get some screwy number with lots of decimal places.

 Avedas 01-21-2013 04:46 AM

Quote:
 Originally Posted by jrcsgtpeppers no, i pick up 6 cards and keep them all in my hand, no replacement. how do i use combinations? is the above sir correct though?

didn't really look over his math but i don't think he's right, just from his approach.
if you're doing probability you need to read and understand this or you're boned, honestly. don't worry about pascal's triangle. i'm pretty rusty on the mechanics so i'd probably make a stupid mistake if i tried.

 JimDawson 01-21-2013 04:55 AM

^ Yeah, it's wrong. I didn't take into account that as you're drawing cards, the overall number of cards changes. That makes it more complicated. That's only one of the things which don't add up. It has to be some kind of calculation which can't exceed 1 or 100%, and the only basis I have to go on from experience is an equation to figure out note pitches if A4=440Hz.

Right now, I am trying to mutilate this formula:

X= 440*2^(y/12)

I'm still going hard at it, but I am pretty sure you need some kind of fractional exponent to make it work.

 jrcsgtpeppers 01-21-2013 04:57 AM

explain this? i think its the formula i have to use

 willT08 01-21-2013 04:58 AM

It's not. In that, n is the number of terms and r is the ratio. That's for either geometric are arithmetic progressions, I forget which. Probably arithmetic.

 Avedas 01-21-2013 04:59 AM

Quote:
 Originally Posted by jrcsgtpeppers explain this? i think its the formula i have to use

it's the equivalent of nCr or n choose r formula. think of it this way: if i have n cards in a deck, how many different ways can i choose a hand of r cards? so if you have a deck of 4 cards and you want to draw 2 cards, there are 6 different ways you can draw 2 cards.
Quote:
 Originally Posted by willT08 It's not. In that, n is the number of terms and r is the ratio. That's for either geometric are arithmetic progressions, I forget which. Probably arithmetic.

it is the formula he needs. it's simplified into every calculator ever as nCr though

 willT08 01-21-2013 05:01 AM

Ooops, maybe I monged out. Christ, I got a B in A-Level Maths not 7 months ago...

 Avedas 01-21-2013 05:07 AM

a bit of an example to help:

you have a deck of 40 yugioh cards. you want to draw exodia on your first turn and win the game. so on your first turn there are 5 specific cards you need to get.

from 5 specific cards, you must choose all 5 of them.
this divided by the total number of ways to choose 5 cards from a deck of 40

(5 choose 5)/(40 choose 5) = 1.5197x10^-6 = 0.00015197%

that's a low chance, by the way

also remember 0! = 1 if you happen to need it

 SlackerBabbath 01-21-2013 05:09 AM

Quote:
 Originally Posted by jrcsgtpeppers id like to think that too, but im sitting here thinking, whats the best way to beat all these spoiled rich kids in yugioh after their parents buy them boxes of the new pack series that just came out, and i thought, lets use math! then i remembered i never took stats :sad:

Knowing the odds is one thing, being lucky enough that the odds work in your favour or knowing how to manipulate the odds are both something else entirely.

 Avedas 01-21-2013 05:14 AM

Quote:
 Originally Posted by JimDawson Right now, I am trying to mutilate this formula: X= 440*2^(y/12) I'm still going hard at it, but I am pretty sure you need some kind of fractional exponent to make it work.

if you want to solve for y you'll need to use logarithms, then it's quite simple.

x = 440*2^(y/12)
log x = log 440*2^(y/12)
log x = log 440 + (y/12)log 2
(log x - log 440)*12/log 2 = y

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