Monday Math Madness #10: Feeling Lucky?
07 Jul 2008 Quan Quach 7 comments 3162 views
The Problem Statement
Update: The family mathematician is an idiot and has been relieved of his duties. It was recently discovered that the probability of winning the lottery at least once during the 25 year stretch is actually 211/243 (instead of 544/625, as previously stated). Special Thanks to TwoPi for noticing the error.
In the Quach family, there is an age-old tradition that has been intact since the 1500s. In this tradition, every member of the Quach family receives one lottery ticket for his/her first 25 birthdays.
Based on empirical data collected over the years, it was determined by the family Mathematician that the probability of a Quach family member winning the lottery at least once during that 25 year stretch is 211/243.
Assuming the above statement is true, what is the probability of a Quach family member winning the lottery at least once during any 5 year interval? (Assume that lottery wins are completely independent of each other).
The Bounty
Winner gets to choose their choice of the following choices:
The Rules
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Email your answers to mondaymathmadness at gmail dot com.
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The winner will get to choose from the collection of literature provided by Mensa. The number of winners will depend on the number of total submissions received
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Depending on how many submissions we receive, we will be giving out additional prizes, giving you yet more chances to win. We’d also like to give a prize out to the “best” or “most creative” answer.
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Inelgible for any one person to win more than once per year. But you should still submit your answer!
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Answer must be explained. You must show your work! We will accept answers in the form of a MATLAB script as well. We will be the final judge on whether an answer was properly explained or not.
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The deadline to submit answers is July 14th 2008, Monday 11:59 PM Pacific Standard Time
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The winners will be chosen randomly from all the submittals using a random number generator.
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The winner will be announced at 9:00 AM PST July 25th, 2008.
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Comments for this post should only be used to clarify the problem. Please do not discuss ANY potential solutions.
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Please spread the word about our contest by stumbling this webpage!
7 Responses to “Monday Math Madness #10: Feeling Lucky?”
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Include MATLAB code in your comment by doing the following:
<pre lang="MATLAB">
%insert code here
</pre>
So far, there has only been one submittal. Either this problem is too difficult, or people are losing interest in MMM!!!! Or maybe the prizes suck. What is going on?????
It is certainly not too difficult. I solved it within 5 minutes. And that’s not because I work with these kind of problems every day or something like that.
So, I solved it already, although I didn’t submit my answer yet. Maybe there are more people like me who wait to send in for some reason? So I don’t think it’s because of the difficulty or the prizes. Anyway, the less people submitting, the more chance I have to win! :-p
This seems way too easy. I don’t understand why the previous number was an error though. It would have been just as easy to solve.
Did I miss something?
- Alex
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Alex: Indeed, the original numbers lead to a solution just as readily as the modified ones. The original problem led to an irrational solution, and from context I suspected that the intent had been for the solution to be “nice”. I sent an email asking if there’d been a typo, and lo and behold apparently there was.
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