Author Topic: Is anyone good with probability?  (Read 502 times)

TheTSKoala

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Is anyone good with probability?
« on: September 22, 2015, 08:34:56 AM »
Trying to work this out.. but I've always been terrible in statistics.  And we have a random assortment of people here that are awesome at all sorts of stuff, so I figured it was worth a shot.

You have 4 decks.  You draw 1 card from each deck.

First Deck of 6 cards.  2 cards have an X on them.  (1:3)
Second Deck of 8 cards.  3 cards have an X on them.  (3:8 )
Third deck of 10 cards.  5 cards have an X on them.  (1:2)
Fourth deck has 12 cards.  6 cards have an X on them.  (1:2)

What the bloody hell is the equation to find out the odds of drawing 2 Xs from 4 cards?  lol  

Bonus question.  How would you write in the odds of 1 card in the 8 deck having two X's.  And 2 cards of the 10 and 12 deck also having two X's.  

And.. "Koala, what the heck are you up to?"  Trying to solve an inter-office discussion.
« Last Edit: September 22, 2015, 08:36:37 AM by TheTSKoala »

Morgenstern

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Re: Is anyone good with probability?
« Reply #1 on: September 22, 2015, 08:54:43 AM »
Before I crunch, is the question chance of drawing exactly 2 Xs, or 2-or-more Xs?
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TheTSKoala

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Re: Is anyone good with probability?
« Reply #2 on: September 22, 2015, 09:05:19 AM »
Before I crunch, is the question chance of drawing exactly 2 Xs, or 2-or-more Xs?

2 or more.  And thanks!

Morgenstern

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Re: Is anyone good with probability?
« Reply #3 on: September 22, 2015, 09:07:03 AM »
The 3rd and 4th decks together create a very manageable space -

1 of 4 outcomes no Xs, 2 of four outcomes 1 X, 1 of four outcomes 2 Xs

The first two decks are a bit trickier, but still easily computed together

3 of 24 outcomes are 2 Xs, 11 of 24 outcomes are 1 X, the remaining 10 outcomes are 0 Xs.

Now combining the 2 to produce 96 outcomes where~

Outcomes where Set A produces 0 and Set B produced 2 = 3 (1x3)
Outcomes where Sets A and B produced 1 each = 22 (2 x 11)
Outcomes where Set A produces 2 and Set B prduces 0 = 10 (1 x 10)

For a total of  35 out of 96 possible outcomes or 36.458333% chance.
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Morgenstern

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Re: Is anyone good with probability?
« Reply #4 on: September 22, 2015, 09:07:40 AM »
Before I crunch, is the question chance of drawing exactly 2 Xs, or 2-or-more Xs?

2 or more.  And thanks!

Oh. Now you tell me you want the EASY answer ;). One sec.
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Morgenstern

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Re: Is anyone good with probability?
« Reply #5 on: September 22, 2015, 09:16:17 AM »
Merging the sets looking for NOT 2+ Xs, we get

Outcomes where both set A & B produced 0 = 10 (1 x 10)
Outcomes where Set A produced 0 and Set B produced 1 = 11 (1 x 11)
Outcomes where Set A produced 1 and Set B produced 0 = 20 (2 x 10)

41 out of 96 outcomes are less than 2.
55 out of 96 outcomes (57.291666%) are 2 or greater.
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TheTSKoala

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Re: Is anyone good with probability?
« Reply #6 on: September 22, 2015, 09:20:19 AM »
You rock!  I owe you an Innis and Gunn!

Morgenstern

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Re: Is anyone good with probability?
« Reply #7 on: September 22, 2015, 09:38:08 AM »
The double X cards are a pain in the ass, but still doable :).

Set A becomes 12 outcomes~
3 outcomes of 0
5 outcomes of 1
3 outcomes of 2
1 outcome of 3

Set B is still 24 outcomes but~
10 outcomes of 0
9 outcomes of 1
4 outcomes of 2
1 outcome of 3

Merging sets (288 outcomes) looking for less than 2 we get~

Outcomes where both set A & B produced 0 = 30 (3 x 10)
Outcomes where Set A produced 0 and Set B produced 1 = 27 (3 x 9)
Outcomes where Set A produced 1 and Set B produced 0 = 50 (5 x 10)
107 out of 288 outcomes are less than 2.
181 out of 288 outcomes (62.847222%) are 2 or greater


  I'm not sure what an Innis and Gunn are... :)
« Last Edit: September 22, 2015, 09:44:14 AM by Morgenstern »
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TheTSKoala

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Re: Is anyone good with probability?
« Reply #8 on: September 22, 2015, 09:45:45 AM »
The double X cards are a pain in the ass, but still doable :).

Set A becomes 12 outcomes~
3 outcomes of 0
5 outcomes of 1
3 outcomes of 2
1 outcome of 3

Set B is still 24 outcomes but~
10 outcomes of 0
9 outcomes of 1
4 outcomes of 2
1 outcome of 3

Merging sets (288 outcomes) looking for less than 2 we get~

Outcomes where both set A & B produced 0 = 30 (3 x 10)
Outcomes where Set A produced 0 and Set B produced 1 = 27 (3 x 9)
Outcomes where Set A produced 1 and Set B produced 0 = 50 (5 x 10)
107 out of 288 outcomes are less than 2.
181 out of 288 outcomes (62.847222%) are 2 or greater


  I'm not sure what an Innis and Gunn are... :)

It's a Scottish Ale.  Very nice for slow drinking over a game session.

Krensky

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Re: Is anyone good with probability?
« Reply #9 on: September 22, 2015, 10:16:14 AM »
Would you trust a marsupial that drinks euchalyptus dorflingers like they were water?
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Gentry

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Re: Is anyone good with probability?
« Reply #10 on: September 22, 2015, 05:54:34 PM »
I'm just glad he switched to those from the eucalyptus harvey wallbangers. Whoa.
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Krensky

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Re: Is anyone good with probability?
« Reply #11 on: September 22, 2015, 06:32:02 PM »
How on Earth is vodka, orange juice, and galliano worse than absinthe, gin, and orange bitters?

Seriously...
« Last Edit: September 22, 2015, 06:34:32 PM by Krensky »
We can lick gravity, but sometimes the paperwork is overwhelming. - Werner von Braun
Right now you have no idea how lucky you are that I am not a sociopath. - A sign seen above my desk.
There's no upside in screwing with things you can't explain. - Captain Roy Montgomery

foproy

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Re: Is anyone good with probability?
« Reply #12 on: September 23, 2015, 10:29:19 PM »
since the behavioral sciences department were slipping Lysergic acid diethylamide into his oj.
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