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Probability

 
 
Reply Wed 31 Aug, 2016 01:57 pm
What is the probability that a waitress will refuse to serve alcoholic beverages to serve alcoholic beverages to serve two minors if she randomly checks the I.D's of five students from among nine students of which four are not legal age?

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Reply Wed 31 Aug, 2016 02:47 pm
@lemiumeta,
Do you mean "at least two minors" or "exactly two minors"?

There are 9c5 total combinations (9!/5!/(9-5)!) = 126
There are 5c5 combinations in which no minors get carded = 1
There are 5c4 x 4c1 combinations in which one minor gets carded = 20
There are 5c3 x 4c2 combinations in which two minors get carded = 60

So 81 times out of 126 at least two minors get away or 61%.
60 times out of 126 exactly two minors get away or 48%.
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