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May 9th, 2011, 10:36 PM   #1
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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.)
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May 9th, 2011, 11:58 PM   #2
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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%.
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May 10th, 2011, 10:15 AM   #3
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Re: A Card Probability

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May 10th, 2011, 08:56 PM   #4
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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.
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May 10th, 2011, 09:14 PM   #5
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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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