|Instructor:||Mr. Ahmed Hefny|
|Attendance:||Ayan, Adan, Areej, AbdulRafay, Bilal, Baseer, Omar|
|Handout:||Pre-Algebra Chapter 1|
|Problems Solved in Class:||* Probability problems: throwing a die and drawing from a deck of cards.|
* Disproving false statements about properties of operators: commutative and associative properties of subtraction, addition distributes over multiplication.
|Concepts:||[Session 1] A brief introduction to probability:* Probability and statistics are two opposite inference paths; probability tells us, given knowledge about a random process, how to answer questions related to samples from that process. [Ex: what is the probability of getting 3 heads in a row if I throw a fair coin three times ?]. Statistics tells us, given a sample from the random process, how to gain knowledge about that process. [Ex: Given a sample of 10000 voters, how much is the American community biased towards Republicans ?]|
* Basic probability laws and the conditions for their correctness: Let A and B be two conditions (usually called events)
- P(A) = # of outcomes that satisfy A / # of all possible outcomes [Assuming all outcomes are equally likely]
- P(A and B) = P(A)P(B) [iff A and B are independent]
- P(A and B) = P(A)P(B|A) [P(B|A) is the probability of B happening given that A happened. P(B|A) = P(B) iff A and B are independent]- P(A or B) = P(A) + P(B) [iff A and B are disjoint i.e. A and B cannot happen together]- P(A or B) = P(A) + P(B) - P(A and B) [This is the same inclusion-exclusion principle for counting the union of two sets]
[Session 2] Pre-algebra:
- Commutative property- Associative property
- Distributive property
- Disproving a property by a counter-example
- Negation vs subtraction. Negation is a unary operator (takes one number) and gives its negative. Subtraction is a binary operator (takes two numbers) and returns the difference. They happen to use the same symbol '-' but they are different things.
|Notes:||You can access video resources at: https://www.artofproblemsolving.com/videos/prealgebra|
Videos related to today's session are the first four videos of chapter 1.