Harvard Fat Chance: probability from ground up

[EmbraceLife]

most novel contribution of this course

intuitive introduction to counting with many examples
interesting counting problems and puzzles explained with counting and probability concepts
illuminating introduction to normal distribution and central limit theorem

Introduction

Keywords

statistics, probability, counting, language, practice, high school math

Counting

Keywords

counting, rule 1 and rule 2 derived from finger with transformation

counting practices

counting even numbers

Large numbers

Keywords

large numbers, exponential notations, scientific notations

Multiplication rule

Keywords

multiplication rule

More multiplication rule

Keywords

multiplication rule with factorial

The subtraction principle

Keywords

subtraction rule with more complex practices

Counting Collection

keywords

sequences, collections

Application of Collection

keywords

how sequence counting and collection counting work together

Binomial coefficient

keywords

binomial theorem, pascal triangle

multinomials and practice

keywords

how to count ways for n object splitting into two or more groups

Collection with repetition

keywords

how to do collection count while allow repetition

coin flipping with intro to probability

keywords

move from counting to probability or ratio

rolling die

key questions

How to understand probabilities behind rolling die

poker probability

key questions

how to understand probabilities behind poker

Bridge hands and birthday paradox

key questions

How much wrong our intuition or common sense expectation can be in the light of dealing cards and birthday paradox problem?

Expectation

key questions

how to understand expectation in gambling games

Expected value slot machine

key questions

relation between outcome, payoff and probability
how to understand the probability behind slot machine

Expected Value Strategizing

key questions

Expectation can help decisions but with many constraints
how to compare many games for the best one using Expectation?

The Monty Hall problem

Key questions

how to understand Monty Hall problem with conditional probability?

Conditional probability setup and examples

key questions

to understand conditional probability with total probability of sum

Conditional probability with election

key questions

How to understand and use bayes rule?

Bernoulli trials

key questions

how to understand bernoulli trials from flipping coins examples

Gambler's ruin

key questions

what if we don't know how many trials to do, then we can't use bernoulli or binomial trials
how to find out the probability of winning, only given p(win), a(initial capital), b(capital goal), a down to 0 = end game

Games

key questions

how to calc expectation value and variance
properties of ev(G + c), ev(G x d), var(G+c), var(G x d)

Example and variance

key questions

how to calc variance (not very illuminating)

The iterating game

key questions

how to calc prob of flipping coin large number of times
quick formula for calc G(n)'s mean and variance

The normal distribution

key questions

the practical purpose of normal distribution from coin flipping view
why we need standard normal distribution or bell curve

Interesting point

large number of averages: chance of getting 600 or more heads of 1000 flips is much much less than chance of getting 60 heads from 100 flips

practice

a very comprehensive problem solution to use normal dist to calc 520 heads or more from coin flipping 1000

The normal distribution part 2

video links

original course video

Key questions

how to calc probability between two payoff values?
intuitive introduction to central limit theorem

• extend normal distribution to calc probability of large iterations of any game

practice

very comprehensive problem solution to exten normal distribution to huge number of iterations of any game
how to use Z-table