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MATH 119 – GOODIES FOR PART 2

COINS EXTRA CREDIT

OR

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:

DICE GRID

VIDEO WITH CARD GRID

OTHER GOODIES – PART 1

What is random?  Great videos!!

Law of Large Numbers (coin simulations)

Flipping coins

Dice

Cards (with a fun intro)

OTHER GOODIES – PART 2

Lesson 13: Independence and “Casino” (Warning: Profanity!)

Lesson 14: Conditional Probabilities

• COOL "BIRTHDAY PROBLEM" APPLET!! ALSO, THE CHARTS I USED TO FIGURE OUT MY PROBABILITY OF WINNING (?) MY BET.

Birthday List (list of probabilities)

Lesson 16: Expected Value and “Don’t Be a Gambling Addict!”

• THE SAD TALE OF MR. AKIO KASHIWAGI

Depiction in “Casino”:

Article on Kashiwagi (“The Warrior”) and “The Donald”:

• “MOLLY’S GAME”; Harlan: Going full tilt

(WARNING: PROFANITY!)

Lesson 16: Expected Value and “Deal or No Deal”

• 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).

Lesson 17: Counting

Lesson 18: Binomial Probabilities (Excel)

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).

Monty Hall (3-Door) problem

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)

100 doors

Variations

http://www.cut-the-knot.org/hall.shtml

Monty Hall analysis

Compare the observed relative frequency distribution with the theoretical (binomial) probability distribution.

Use 0.67 for p.

Monty Hall handout

Monty Hall distribution (Excel)

Explaining Monty Hall

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!)

Plinko / Pascal’s Triangle (theory for the Binomial Formula)

"The Wall" - a more modern version (but no sliding!)

The Beauty of Pascal's Triangle

The Magic of Pascal's Triangle (Plinko from The Price is Right and Word Jumbles)

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?

See Chaos and Fractals by Peitgen, et al:

Play with this!  Let n = Size = # of questions.

Each ball corresponds to a student.

Each drop corresponds to a question.

Move Right = get the question “right” from random guessing.

Move Left = get the question wrong from random guessing.

Left/Right corresponds to q and p.  For an A, B, C multiple-choice test, use Left = 67%, Right = 33%.

Bottom axis = # of questions correct.

#s on bars = frequencies (#s of students).

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.)

RANDOMNESS

Poisson scatter – Raindrops, Bombing London, Glowworms - life isn’t fair!

Our Sense of Probability

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)!

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.)

Gambler’s Fallacy (related to #1 in “Sense”)

• “MOLLY’S GAME”; Harlan: Going full tilt

(WARNING: PROFANITY!)

GREAT BLOG: