## Sunday, March 13, 2016

### Division M2 session on March 13, 2016

 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. Student Difficulties: Thinking in terms of equations Generalizing distributive property to arbitrary operators. Homework: Download PDF Note: There are some hints in the end of the file. Try to solve first without looking at them. Notes: You can access video resources at: https://www.artofproblemsolving.com/videos/prealgebraVideos related to today's session are the first four videos of chapter 1.