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Archive for the ‘Problems’ Category

GeoGebra: Binomial Distribution with Normal and Poisson Approximation

June 6th, 2011 4 comments
Click the image to link to GeoGebraTube
(Opens in a new window/tab).

This applet is for visualising the Binomial Distribution, with control over n and p.

It also shows the Normal Approximation curve (and how this approximation breaks down for large or small p)
and it shows the Poisson Approximation curve (and how his approximation breaks down if there’s no positive skew)

You can show critical regions at either end by turning the bars red instead of green. The appropriate cumulative binomial probabilities are shown.

The Shrinking Square

February 19th, 2010 1 comment

Fullscreen capture 19022010 221332.bmp

Problem:
When the area of the green square is two-fifths of the area of the whole diagram, what fraction do the four black triangles occupy?

Open the post to play with a Java applet.

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The Trapezoid Trap

October 1st, 2009 3 comments

What is this shape called?

TrapezoidTitleImage

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Folding a Trapezium: Solution

September 27th, 2009 2 comments

A Geometric Secret of A4 Paper

Trapezium-A4-1-1024x819

Problem:

We wish to make two folds in a rectangular piece of paper to form a trapezium (or trapezoid for the chaps across the water).  Read more…

“Higher or Lower” – Part II

September 13th, 2009 10 comments

classic-playing-cards

In Part I we calculated the probability of winning a single-suit version of the Higher of Lower card game.  The objective of this post is to find the probability of winning the full, unsimplified, 4-suit version of the game played in pubs across the land. Read more…

“Higher or Lower” – Easy card game? Part I

September 5th, 2009 3 comments

Higher or Lower

I was recently roped into joining some friends for a pub quiz.  I hate pub quizzes.  For a start, I don’t watch soaps or football or take any interest in divorcing celebrities.  The sum total of my contribution is usually a question about the periodic table and another about some obscure ’90’s one-hit wonder.

At the end of this particular quiz there was a competition to win a pot of dosh.  Those optimistic enough to enter first had to be lucky enough to have their number drawn from a hat, and then attempt to win the ominous game of Higher or Lower, or “Play Your Cards Right” as it is sometimes known, via a crudely written flash program running on the host’s laptop.  If you win the game, you win the cash.  Easy?  Apparently not.  Two players failed in succession and then the host declared that the contents of the pot would roll over to next week.  Almost everyone in the pub had just lost a quid.  Would anyone ever win the money?  I didn’t know, but I was alarmed and it was my duty to discover the probability of winning this game.

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Folding a Trapezium (Problem only)

August 26th, 2009 No comments

A Geometric Secret of A4 Paper

Trapezium A4-1

I’m not just going to give the answer away this time!  At least not for a while anyway… (Click here for the solution) Read more…

Mathematical Mice – Part I

August 21st, 2009 4 comments

Mrs Farmer is frightened of mice.  One day she finds 3 mice in her kitchen.  She tries to scare them out, but these are no ordinary mice…

Mice Think Dice

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Hallucinogenic Maths – The 1-in-10 Gay Problem Concluded

August 17th, 2009 2 comments

Visualising imaginary forms…

complex_circular_vectors

This post builds further on the concepts discussed in the original 1-in-10 Gay Problem post and its sequel, Find a way to my Heart, and delves deeper into the abstract to discover an impressive 3d form hidden in our function.  It will be assumed that the reader has studied these preceding posts (10 minutes’ fascinating reading!) Read more…

Find a way to my Heart: The 1-in-10 Gay Problem Continued…

August 4th, 2009 1 comment

This post builds on the ideas from the first 1-in-10 Gay Problem post and takes a step into the creative world of abstract maths.

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The 1-in-10 Gay problem!

July 28th, 2009 3 comments

…a maths problem that is.

“If 1-in-10 people are gay, and there are 10 people in a room, one of the people in the room must be gay!”

Is this true?  Take a look here for the full analysis!

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