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MATH 119 – GOODIES FOR PART 2
COINS EXTRA CREDIT
You may use the handout I gave out in class - or if you missed class, the attached .docx or .pdf file. When turning in your work with your name, you may use another appropriate file that you make. Make sure NOT to indicate which group you are in - someone else is supposed to figure it out.
If you did not pick a card in class, have random.org flip a coin for you and then follow the instructions on the handout. Let heads = black card; tails = red card.
Here is a link that will help (especially if you drew a black card in class or got “heads”):
If that site’s down, try:
VIDEO WITH CARD GRID
OTHER GOODIES – PART 1
What is random? Great videos!!
Law of Large Numbers (coin simulations)
Roulette (about Roulette; our videos!)
Cards (with a fun intro)
OTHER GOODIES – PART 2
Lesson 18: Binomial Probabilities
Poisson scatter – Raindrops, Bombing London, Glowworms - life isn’t fair!
Our Sense of Probability
Gambler’s Fallacy (related to #1 above)
• Molly’s Game: Harlan: Going full tilt (WARNING: PROFANITY!)
FUN CLASS LINKS FROM LESSON 18 -
BINOMIAL DISTRIBUTIONS and MONTY HALL
Flipping coins - good examples of binomial distributions!
When you flip 100 fair coins and count heads, you’re sampling from Bin(n=100, p=1/2).
D!ng (from class)
In class, we sampled from Bin(n=18, p=2/3).
Play it! Or have the computer play it (see the "Repeat" line)! (Rossman/Chance applet)
Lots of YouTube links
Monty Hall analysis
Monty Hall handout
Plinko / Pascal’s Triangle (theory for the Binomial Formula)
"The Wall" - a more modern version (but no sliding!)
The Beauty of Pascal's Triangle (See Notes 4.12)
The Magic of Pascal's Triangle (Plinko from The Price is Right and Word Jumbles)
See Chaos and Fractals by Peitgen, et al:
QUINCUNX ("PLINKO") APPLETS AND SITES
http://www.jcu.edu/math/isep/Quincunx/Quincunx.html (This applet's better.)
http://en.wikipedia.org/wiki/Bean_machine (Wikipedia article)
http://en.wikipedia.org/wiki/Quincunx (Wikipedia article)
Binomial Distribution: Gallery of Binomial Histograms
• FUN WITH PASCAL'S TRIANGLE (THEORY: BINOMIAL FORMULA)
• BINOMIAL HISTOGRAMS
Binomial Distributions (Produced with Mathematica and Microsoft Word with MathType.)
• YOUTUBE GAME SHOW LINKS
• Greed (going for $2.2M!!): http://www.youtube.com/watch?v=9NWDl21PSY0
• Super Greed ($2M question): http://www.youtube.com/watch?v=zQxCu4Pqp2U&feature=related
• Big risk on Deal or No Deal (a special episode with multiple $1M cases): http://www.youtube.com/watch?v=MQ40bwT-0fU. Think about the banker’s offers. We’re going to discuss them. If you were the player, what would you have done?
Deal or No Deal - Australia (watch the video, think about “the odds of
that …,” and then read the description).
• The Price is Right / Plinko winner (the Plinko board is in the second half): http://www.youtube.com/watch?v=vuMir11YFPs. What does this have to do with Pascal’s triangle?
GAMES DAY 2:
• COOL "BIRTHDAY PROBLEM" APPLET!! ALSO, THE CHARTS I USED TO FIGURE OUT MY PROBABILITY OF WINNING (?) MY BET.
Birthday List (list of probabilities)
The Difficulty of Faking Data (by Theodore P. Hill. Coin runs and Benford's Law - very unexpected!)
If you like to trick or manipulate people, check out my "Great Books" link below (especially Plous)! Click here
GAMES DAY 1:
Coin Flips (Extra Credit) (given in class)
Applet: (Play the game with the computer keeping score!)
Monty Hall Web Sites:
http://www.youtube.com/watch?v=mhlc7peGlGg (complete explanation)
http://www.cut-the-knot.org/hall.shtml (includes variations)
(Deep thoughts and interesting perspectives from a renowned mathematics writer.)
(Goes deeply into the probability behind this!)
• MONTY HALL STATS
http://www.kkuniyuk.com/Math119MontyHallAnalysis.pdf – compare the observed relative frequency distribution with the theoretical (binomial) probability distribution
Information on the cognitive psychology we discuss in this class.
http://en.wikipedia.org/wiki/List_of_cognitive_biases (List of cognitive biases)
http://en.wikipedia.org/wiki/Amos_Tversky (Tversky was one of my profs.)
• OUR SENSE OF PROBABILITY
• THE SAD TALE OF MR. AKIO KASHIWAGI
ASK GOOD QUESTIONS
Email me (I encourage corrections!)