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February 18th, 2012, 03:30 AM  #1 
Newbie Joined: Feb 2012 From: The Netherlands Posts: 2 Thanks: 0  Probability formula
Hello, Probably a simple question here, but my math fu is weak: Say I have a standard deck of 52 playing cards (13 of each suit), and I randomly draw 7 cards. What are the odds I draw at least 3 Hearts cards? I'm mostly interested in how to calculate it, not so much the answer to this specific question. It's the 'at least' bit that stumps me. Any and all help much appreciated! 
February 18th, 2012, 05:58 AM  #2 
Senior Member Joined: Oct 2011 From: Belgium Posts: 522 Thanks: 0  Re: Probability formula Clear when you see the formula? 
February 18th, 2012, 06:14 AM  #3  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Probability formula Hello, Probably! Quote:
"At least 3 Hearts" means: 3 Hearts or 4 Hearts or 5 Hearts or 6 Hearts or 7 Hearts. [color=beige]. . [/color]We must compute each probability separately then add them. To save time and energy, consider the opposite event: "at most 2 Hearts". [color=beige]. . [/color]This means: 0 Hearts or 1 Heart or 2 Hearts. 0 Hearts There are 13 Hearts and 39 Others. We want 7 Others. 1 Heart We want 1 Heart, 6 Others. 2 Hearts We want 2 Hearts, 5 Others. [color=beige]. . . . . . . . . . . . . . . [/color]  
February 18th, 2012, 07:47 AM  #4  
Newbie Joined: Feb 2012 From: The Netherlands Posts: 2 Thanks: 0  Re: Probability formula
That's a great explanation, thanks! I was trying to find a way to just plunk all the numbers into a single formula, so I could've been searching for a way to do that for ages with no result... It seems so obvious now, but I'd never have figured it out by myself. Quote:
 
February 18th, 2012, 06:57 PM  #5  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,686 Thanks: 701  Re: Probability formula Quote:
Couldn't figure out why. Decided to check up on Soroban: 39choose7 = 15,380,937, not 7,285,707. Make that change in Soroban's calculations and all is fine: .23231737... is the result, or ~23.2 Go stand in the corner, Soroban  

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