COMPSCI C8 Lecture 6: Week 6 Study Guide (Lecture & Textbook Notes)

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Department
Computer Science
Course
COMPSCI C8
Professor
John Denero
Semester
Spring

Description
CS8 Weekly Study Guide  Week 6: Chance, Sampling  Monday, February 20 - Friday, February 24 CIT Readings:  ● 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,  we have  ○ 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 
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