At an obscure drill meet somewhere in Area 4, a Naval Science Instructor walks into the classroom being used by Middletown High School's crack drill team. He looked around and noted that there were exactly 12 cadets in the room, none of whom were doing anything useful. The rest of the crack drill team was hanging out in the cafeteria doing nothing useful--you can see the trend, but that's another story. The NSI picks a cadet, puts a dollar on the table, and says, "Cadet, I don't know anything about any of you, but I'll bet you this dollar that there are at least two cadets here who share the same birth month." The cadet takes the bet.
Did the NSI make a good bet? Your answer must include the probability of the NSI winning the bet. There are no tricks. (Incidentally, betting that no Middletown cadet will attempt to answer a question such as this because it requires a little math and actual effort would be a good bet!) This challenge will close-out on Wednesday, 23 November at 0730.
Happy Birthday, weasels! Good Luck!
HERE'S PART II
Here's the second part. Good luck--especially since no one got the first part.
Anyway,after confounding the cadets in the classroom, the NSI walks down to cafeteria where the rest of the lazy cadets are hanging out. There he sees them: five Middletown cadets doing nothing useful. He walks over and offers them the same bet, to wit: I'll bet you a dollar that at least two of you five share the same birth month. Would this be a good bet? Your answer must include the probablity, a discussion of how you derived the the answer, and a simple summary of why it would or would not be a good bet.
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