CS8 Weekly Study Guide
Week 6: Chance, Sampling
Monday, February 20 - Friday, February 24
● Mon: Holiday
● Wed: 8.3, 8.4
● Fri: 8.5
LEC 15 (WEDNESDAY): Chance
● Most probabilities are relative frequencies
● Simulation can be an important tool in determining probabilities.
● We will use the standard notation P(event) to denote the probability that "event"
happens, and we will use the words "chance" and "probability" interchangeably.
● Complement rule: Chance That Event Does NOT happen = 1 - chance it does
● Multiplication rule: Chronological Order: Multiply the probabilities.
○ Think of this as a “fraction of a fraction” so the probability number gets smaller
○ P(two events both happen) = P(one event happens)×P(the other
event happens, given that the first one happened)
● If order does not matter, you may partition the outcome into “ways it could happen”. Thus,
○ Addition Rule: P(an event happens) = P(first way it can
happen)+P(second way it can happen) provided the event happens
in exactly one of the two ways
○ Think of this as a sum of chances: the more ways it can happen, the more likely
and it will be a bigger number due to addition
● The Monty Hall Problem