1.1 Course introduction

What is probability?

Source: Merriam-Webster

Pierre-Simon Laplace

Laplace

Analytic theory of probabilities

Which one is more likely?

Roll one (six-sided) die 🎲

  • Getting an even number
  • Getting an odd number


Roll two dice 🎲 🎲

  • Getting a sum of 7
  • Getting a sum of 12

Roll three dice 🎲 🎲 🎲

  • Getting a sum of 11
  • Getting a sum of 12

“Probability is common sense reduced to calculation.”

Pierre-Simon Laplace

What is statistics

How to collect, analyze, present, and interpret data

  • Probability
    • If I toss a fair coin 5 times, how likely to receive 5 heads in a roll?
  • Statistics
    • I just tossed a coin 5 times, and received 5 heads in a roll. Is it a fair coin?

Probability vs statistics

Probability
(Deductive reasoning)

Statistics
(Inductive reasoning)

Population
(or hypotheses)

Sample
(or data)

Airline travelers’ club

  • An airline offers an executive club and claim that 10% of its customers would qualify for the membership.
  • You suspect it is actually less than 10%.
  • You randomly selected 1000 customers, and found 91 of them would qualify.
  • Is the airline’s premise correct?