Archive for the ‘probability’ Category

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OMG! Credit Card Antenna Geometry is so cool + some PIN Probability

January 24, 2023

The world  has mostly agreed on the size of a credit card:

Credit cards today contain a microchip and aerial.

A credit card is dissolved in ACETONE (solvent found in some nail polish removers) to extract the chip & aerial in this BBC video.

 

OMG! It still works to pay for coffee but if you wanted cash you would still need the PIN.

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Stranger Things Math: Eleven and the Galton Board

July 3, 2022

NOTE: Michael (above), who seems appropriately scary for this post, uses a commercial Galton Board.  It has one flaw. Many balls feed into the grid at once and this will change the pathways taken because the balls bump into one another. The best results come from dropping in the balls one at a time. If you had the patience to drop in 3,000 balls one at a time.

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2D Random Walk or doing the Bell Curve Shuffle

July 28, 2021

This is the best Middle School Probability outdoor exercise  EVER!

Equipment:

1 coin per student. 

Instructions:

In the schoolyard, students move back and forward with the flip of a coin. Must be a good flip. This exercise works best with a grid drawn on the schoolyard in chalk, perhaps. (See pic below) If possible film the exercise from above.

Now here are lots of people doing this 2D random Walk on Wall St. The results are totally amazing.

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Watch for the Bell Curve. It’s AWESOME.

This video was made by The National Museum of Mathematics NY.

Check out their Squared wheeled bike here.

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A Bitcoin Bubble, a Random Walk and a blind-folded Monkey

July 6, 2021

What is all this monkey business? It started in 1973 when Princeton University professor Burton Malkiel claimed in his bestselling book, A Random Walk Down Wall Street, that “A blindfolded monkey throwing darts at a newspaper’s financial pages could select a portfolio that would do just as well as one carefully selected by experts.”

In other words, the stock price movement is random. 

See Forbes Magazine here.

Now in its 12th edition, the book tackles Investment Bubbles including Bitcoin. Is there a Bitcoin Bubble? According to the ABC on 24 MAY 2021 this was the Bitcoin Bubble Graph:

From the ABC news here

Random Walk Game

So can you beat the financial market? Try this 2D Random Walk game (pic below) to see if you can guess the next random move and beat the system.

In the game, you have to remove gold blocks by clicking on blocks in the way of the moving green dot, but you lose energy (lose money, perhaps) each time you remove a block.  Can you guess where the green dot is moving? Can you survive? Mmmmm! Good Luck. You’ll need it.

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3D Random Walk Math . . . . . . . . . . . . for Middle School

July 6, 2021

Random Walk math is both simple and complicated all at the same time. The math models are a little bit complicated but the concept is simple. 

Random walk math is used to model many processes in Chemistry, Physics, Biology, Zoology, finance (Stock market movement), psychology, ecology,  computer science, and video games.

Simple Example:

Choices: Up, Down, N, S, E, W.

Note: We are still using constant step size and right-angle turns.

The random walk of one particle would look something like this from Mathworld:

In an infinite no. of steps the probability of reaching the starting point again is 0.3405373296 or about one-third. Mathematicians use math models to calculate the probability of a particle ending up here or there or back where it started. eg. It is less likely that the particle above would move in a straight line 500 times in a row. 

You can play with a 3D random walk generator here.

And check out this excellent video explaining a 3D Random Walk in nature.

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Trick 9: Coin Trick. How to throw 10 HEADS in a row!!!!

April 30, 2018

Requirements: A coin for each student & smart board or data projector.

First ask your students to toss a coin 10 times each.

Ask each student how many heads in a row they threw.

Now ask students ‘Do you think it is possible to throw 10 heads in a row?

It can be done. Here is how you do it.

Derren Brown is a UK mentalist, magician, hypnotist and maths guru. He’s awesome. He shows audiences how a lack of understanding maths, especially probability, leads to misinterpreting the facts.

Now play this video to the students:

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Trick 10: A Foolproof Gambling System

April 23, 2018

Math Mentalist Devises Foolproof Gambling System

Requirements: Smart board/Data Projector

or Chalk & Talk

This is the most awesome way to introduce probability.

Mentalist Derren Brown devises a foolproof gambling system. He sends a girl , Kadisha, the number of a winning horse in race to be run the next day. It wins. He sends her the winning horse and race number 4 more times. She ends up with winnings close to £ 1000 before the final race. Derren convinces her to borrow money for the last bet. She does. She places £4,000 on a horse. Did it win?????

Watch Part 5 of The System

 

 

If you are not convinced Derren Brown can come up with a foolproof system for horse race tipping, let me explain The System. He took 7,776 e-mail addresses, divided them into 6 equal groups and sent each group a different number for a horse in a 6 horse race to be run the next day. Naturally, one group of 1296 had been given the winning horse number.  This group was divided into 6 again and given the number of the ‘winning’ in a six horse race the next day and so on.

Race 1: 7776

Race 2: 1296

Race 3: 216

Race 4: 36

Race 5: 6

Out of 7776 punters, only one punter was given in advance five horse race winners in a row. Was it Kadisha. You will have to watch the Youtube above.

You can watch THE SYSTEM in full here. It takes 47 mins.

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MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig MathsPig …………………………………………………. with Kerry Cue

April 25, 2015

Mathspig Maths Mystery Box

Helloooo My Little Luvvies,

 

So here are the 10 Maths Mystery Box challenges I’ve put together for you:

1. Maths Mystery Box 1: NOT STUPID

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2. Maths Mystery Box 2: CURIOUS

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3. Maths Mystery Box 3: NERD

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4. Maths Mystery Box 4: FUNNY THAT

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5. Maths Mystery Box 5: FANTASY

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6. Maths Mystery Box 6: WEIRD

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7. Maths Mystery Box 7: PHONES

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8. Maths Mystery Box 8: JUNK FOOD

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9. Maths Mystery Box 9: MUSIC

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10. Maths Mystery Box 10: LETHAL

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mathspig bonusAnd the bonus Maths Mystery Box Question:

Sniffer rats have been in the news this week, but:

 When is a sniffer rat better than a sniffer dog?

(Hint: It has to do with a measurement?)

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Isn’t MATHS marvelous? And magical too!

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Hoo Roo for now,

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MATHSPIG

 
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Maths Mystery Box 1: Not Stupid

April 10, 2015


Maths Mystery BOX 1

Not stupid. Just, like, lazy.

Mathspig averages quote

I use the quote above to explain to people that Averages don’t mean much. This is a typical response. Really! Wow! Australians have one breast and one testicle!

We live in a culture of Selective Stupidity. Most people can do the basic maths of: + – x % $$$$, but many don’t bother. We leave maths thinking to machines and their algorithms.

???

So you buy 4 choc bars at 50 cents each and, for fun, ask the shop assistant ‘how much?’ They work the answer out on the cash register. They have to record the purchase. Still, how hard would it be to say $2? We don’t even try.

Yet we need maths every day to buy stuff, read timetables, pay bills, cook, understand food labels, take medication and more. Maths is used in sport, driving, gaming, gambling, drinking (ie. alcohol levels) and banking; maths is used in the workplace, the law, politics, advertising, fitness, the travel industry, gardening, the music industry (Royalty payments are a big issue now), watching TV (Download speeds are crucial), Facebook (How many likes?) and more.

The UK maths-promoting charity National Numeracy quotes from research suggesting ‘weak maths skills are linked with an array of poor life outcomes such as prison, unemployment, exclusion from school, poverty and long-term illness’. (Judith Burns, Poor numeracy ‘blights the economy and ruins lives‘, BBC News, 5 March 2012)

Yeah! And ….

Mathspig hot date quote

Josie Gurney-Read in an article Damaging maths mindset holding pupils back,( The Telegraph, UK, 30 Oct 2014) claimed 17 million adults in the UK have poor maths skills and this is costing the economy £20 billion a year.

£20 billion,eh?

The previous article by Judith Burns, above, quoted research by KPMG auditors that put the annual costs of poor numeracy skills in the UK at £2.4bn.

So £2.4 billion, is it?

Who’s doing the Maths HERE?

Who cares? We let these numbers just fly past without thinking about them. We choose to suffer from Selective Stupidity.

To challenge middle school students to think about the numbers they read here are a few tricky questions:

the maths quiz

Look at the following questions and see if you can work out why the maths is totally dodgy.

1. Dumb and Dumber

doll solar

Solar Plus claimed, after a survey of 60 customers, that 99.98% of customers would recommend their product.

What’s wrong with their Maths?

Answer here.

2. Wanna get rich? Look at the Graph, Dude!

Financial advisers around the world wheeled out graphs like the one below to show that investing in the stock market is very secure and that down turns in the market in 2007 were minor. Oh Yeah!

What is wrong with this graph!

Mathspig Maths Mystery Box 1 graph

Answer here.

3. Run a Red Light. 0.9 sec! $234 fine! Is that fair?

pslogo

Look at the maths. How far would a Mazda 3 travelling at 60 kph (37.3 mph) travel in 0.9 seconds? 

Ans here.

4. Can you out run a fireball?

This is a Movie Cliché we see over and over. But is it possible?

Maths Mystery Box 1  outrun fireball

A Fireball travels at 400 m/sec. That’s metres/sec. Now can you do the maths?

Answer here.

5. You could win the lottery! The least drawn numbers are ….

winlottery

If the least drawn numbers are 41, 32, 10, 43, 35 and 20 will picking these numbers improve your chances of winning the lottery?

Answer here.

6. The Equation for the Funniest Joke is:

According to The Telegraph UK the formula for the funniest joke is:

x = (fl + no ) / p

Where

x = funniness of joke

f = funniness of punchline

l = the length of the build-up

n = the amount some falls over

o = the “Ouch” factor of physical pain or social embarrassment

p = power of the punchline

So, what’s wrong with this equation? Ask Weird Al Yankovic.

MAD Magazine Weird Al Marker Tooth_54dce7ae29a8f0.26429747

Ans here.

(Quick Ans: It’s all rubbish. Guess work x cow manure = bulldust. You cannot measure any of these variables. What’s the unit for measuring funniness?)

7. Coconuts kill 150 people a year. Does that sound right?

260px-'BEWARE_FALLING_COCONUTS'_sign_in_Honolulu,_Hawaii

OK. You are not a crazy death-by-coconut research scientists. But have a guess. Are coconuts that dangerous?

Answer here.

8. 9 out of 10 serial killers prefer murdering kids with Emo hair.

funny-emo-bunny-hair

Does this sound reasonable?

Answer here.

Quick Answer: There’s a lot of joke maths out there but some folk take it seriously.

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Maths Mystery Box 5: FANTASY

February 23, 2015

Maths Mystery BOX 5

 

Middle school maths challenge

%, probability and a fight to the death

The REaping mathspig

Hunger Games Maths Survivor 1a

This problem is trickier than you think. You will need this information.

Major Major HINT

Hunger Games Maths Survivor ANSWER 1

Hunger Games Maths Survivor 2

Hunger Games Maths Survivor ANSWER 2

You will find more HUNGER GAMES maths including How long would it take you to bleed to death? here.