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May 9th, 2011, 10:36 PM  #1 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  A Card Probability
First here is the problem: Two cards are selected randomly without replacement. Determine the probability of selecting at least one face card. This isn't homework. (I'm not even a student.) I was helping someone with a basic stats class, which has one short section on probabilities. Nowhere in the text does it have these "at least" problems  only "exactly"s. But, it showed up from the instructor on a review for the test. I'm thinking I could probably figure it out, but my issue is the solution from the instructor was really bizarre and I did not understand it. How would you guys here go about solving this? (And more than one way would be welcome.) I don't really care about the answer itself  just the method. (Call it curiosity to compare with the goofy thing the instructor did.) 
May 9th, 2011, 11:58 PM  #2 
Senior Member Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3  Re: A Card Probability
There are 40 pip cards, and ways to choose two of them. So the probability of choosing 2 pip cards out of the standard 52 is . Therefore the probability of choosing at least 1 face card is or about 41.18%. 
May 10th, 2011, 10:15 AM  #3 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: A Card Probability 
May 10th, 2011, 08:56 PM  #4 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: A Card Probability
@aswoods  Yeah, MarkFL showed me this on another forum as well, except he did (40/52)(39/51) and you're doing combinations, but I get this. I was trying to find a way to use combinations, but I just never thought to go from the "none" point of view. This suddenly seems very simple. (Though I've never heard the term pip.) @greg  still trying to figure this one out. But that's OK  I did ask for more than one method. I'll ponder this a while. Thank you to you both. 
May 10th, 2011, 09:14 PM  #5 
Senior Member Joined: Apr 2011 From: USA Posts: 782 Thanks: 1  Re: A Card Probability
Now, in case anyone wants to figure this out... I don't know exactly what the instructor did because it never got written down and I wasn't following. What you two have done here just seems SOOOO much simplier. He made a tree. I can only imagine he was using that to show 4 possibilities of the 2 cards. Except I saw no divisions to get an actual probability. And then next to the 4 branches of the tree, he had set notations, something like the intersection between something and the compliment of something. I've never seen set notations with a tree and it just looked like a big mess to me. 

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