Souce: https://canvas.ucsd.edu/courses/55106/assignments/syllabus
Section 1.1
There are roughly 240 students in this class. Which of the following is closest to the probability that at least 2 students share the same birthday?
a. 1%
b.
c.
d. 99%
e. 100%
Use of Probability in History
1600s - Gambling
1900s - Quantum Mechanics
1950s - Finance/Stock Market
2000s - Machine Learning
Modern rigorous formulation of probability theory due to Kolmorgorov in 1933.
Common Ingredients In Models of Randomness:
Probability Space
A probability space is a triple (
), where sample space (
) - collection of possible outcomes, i.e. {HH, HT, TH, TT} collection of events (
) - An event is a subset of , i.e. , A=“1st flip is T”={TH,TT}, A=“at least 1 H”={HH,HT,TH}, , probability measure (
)
a function from
satisfying Kolmorgorov’s axioms:
(A disjoint from B (meaning A and B can’t happen)})
= “empty set”
Area(
If is a sequence of disjoint events, then
disjoint means