Instructor:  Mr. Ahmed Hefny 
Attendance:  Ayan, Adan, Areej, AbdulRafay, Bilal, Baseer, Omar 
Handout:  PreAlgebra 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(BA) [P(BA) is the probability of B happening given that A happened. P(BA) = 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 inclusionexclusion principle for counting the union of two sets] [Session 2] Prealgebra:  Commutative property Associative property  Distributive property  Disproving a property by a counterexample  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. 
Student Difficulties: 

Homework: 

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. 
Sunday, March 13, 2016
Division M2 session on March 13, 2016
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