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On Software Engineering, Mathematics

This is a blog about software, some mathematics, and the occasional philosophy. Not necessarily in that order.

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On Software Engineering, Mathematics | hugosereno.eu Reviews
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This is a blog about software, some mathematics, and the occasional philosophy. Not necessarily in that order.
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and philosophy,on mathematics,sleeping beauty,the mu puzzle,non transitive probabilities,crazy guy,sock drawer,finding your birthmate,coin vs die,the flippant juror,the cliff hanger,coach or kasparov,on others,on philosophy,artificial intelligence
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On Software Engineering, Mathematics | hugosereno.eu Reviews

https://hugosereno.eu

This is a blog about software, some mathematics, and the occasional philosophy. Not necessarily in that order.

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1

The Cliff-Hanger

http://hugosereno.eu/blog/2015/05/05/the-cliff-hanger

And Philosophy" href="http:/ hugosereno.eu/feed.xml" /. Joseph is coming from queima das fitas and is a little tipsy. He stands near a cliff doing something. If he takes one more step forward, he falls over the edge. He takes a series of infinite random steps. Either towards the cliff or away . What is his chance of escaping? Let be the probability of moving towards the cliff , and of moving away . Then:. The first few Catalan numbers are 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786.

2

The Flippant Juror

http://hugosereno.eu/blog/2015/07/20/the-flippant-juror

And Philosophy" href="http:/ hugosereno.eu/feed.xml" /. A three-man jury has two members each of whom independently has probability of making the correct decision and a third member who flips a coin for each decision (majority rules) A one-man jury has probability of making the correct decision. Which jury has the better probability of making the correct decision? The winning outcomes for the first scenario (three juris) are:. Hence, the probability of a correct decision is given by:.

3

Non-Transitive Probabilities

http://hugosereno.eu/blog/2015/09/12/non-transitive-probabilities

And Philosophy" href="http:/ hugosereno.eu/feed.xml" /. Sheldon and Penney decide to play a game. They throw a coin three times. If it comes back. Sheldon wins; if the result is. Then Penney wins. Otherwise they both loose. What are their probabilities of winning the game? The belief that if something happens more frequently than normal during some period, it will happen less frequently in the future. Is exactly the same as any other arbitrary sequence of heads and tails such as. Sheldon won 3685 Penney ...

4

One, Two, Three Dice

http://hugosereno.eu/blog/2015/05/13/one-two-three-dice

And Philosophy" href="http:/ hugosereno.eu/feed.xml" /. One, Two, Three Dice. Which one would you bet on? Throw 6 dice and get at least one 6, 12 dice and get at least two 6’s, or 18 dice and get at least three 6’s? Let’s do the math. The probability of throwing 6 dice and getting at least one 6 is:. The probability of throwing 12 dice and getting at least two 6’s is:. The probability of throwing 18 dice and getting at least three 6’s is:. University of Porto and Senior Researcher at INESC TEC.

5

Crazy Guy

http://hugosereno.eu/blog/2015/07/22/crazy-guy

And Philosophy" href="http:/ hugosereno.eu/feed.xml" /. Assume may each ticket is numbered from 1 to 100. Let $p(i)$ be the probability of the $i {th}$ person to enter the airplane sitting on Camille’s place. Note that only one, if any, will ever sit there. Then:. Note that the probability of 1 sitting in Camille’s place is the same as sitting in 2 place, the only way 2 would be forced to move to Camille’s place. In general:. For fun, here’s a Scala program that simulates this puzzle:.

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