Warm- Up #1 Monday, 2/1/2016 Reflect on your first semester in your math class and answer the following questions: Write three new things that you have learned from last semester. Write three things that you have done well from last semester Write three things that you want to improve/achieve/learn from my class this second semester.

Advanced Math: Warm-Up # 2 Tuesday, 2/2 −4 (𝑥−2) + 5 (𝑥−5) 2. 2𝑥 (𝑥−3) + 𝑥−3 (𝑥 2 +6𝑥+9)

Regular Math: Warm-Up # 2 Tuesday, 2/2 1. 2𝑥 7 + 𝑥−3 5 2. −4 (𝑥−2) + 5 (𝑥−5)

Regular Math: The fundamental counting principle worksheet Homework Regular Math: The fundamental counting principle worksheet Advanced: The Tree diagram and the fundamental counting principle packet

Intro to Probability

Overview Probability is the study of random events. The probability, or chance, that an event will happen can be described by a number between 0 and 1: Impossible 0 = 0% 50 – 50 Chance ½ , .5, 50% Certain 1 = 100%

Vocabulary Definition Examples Trial: a systematic opportunity for an event to occur Rolling a number cube Experiment: one or more trials Rolling a number cube 10 times Sample space: the set of all possible outcomes of an event 1, 2, 3, 4, 5, 6 Event: an individual outcome or any specified combination of outcomes Rolling a 3 Rolling a 3 or rolling a 5

The outcomes of an experiment is the way it can happen The outcomes of an experiment is the way it can happen. Outcomes are random if possible outcomes are equally likely. 6 10 12 52

Experimental Probability (inductively) vs Experimental Probability (inductively) vs. Theoretical Probability (deductively)

Theoretical Probability If all outcomes in a sample space are equally likely, then the theoretical probability of event A, denoted P(A), is defined by 𝑷 𝑨 = 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔 𝒊𝒏 𝒆𝒗𝒆𝒏𝒕 𝑨 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒐𝒖𝒕𝒄𝒐𝒎𝒆𝒔 𝒊𝒏 𝒕𝒉𝒆 𝒔𝒂𝒎𝒑𝒍𝒆 𝒔𝒑𝒂𝒄𝒆

Try these… a) b) P(red) P(blue) P(yellow or blue) A A A B B B 1 5 2 5 3 5 B B B 1 4 1 4 1 2

DICE What is the probability of getting an even number? 6 12 P(even) =

H H T T H T T H The Probability of an Event = P(H+T) = 2 = 1 __ __ 4 2 P(Event) = the number of ways it can happen the number of possible outcomes P(H+T) = 2 = 1 4 2 __ __ H H T T H T T H ?

COINS What is the probability of flipping two coins and getting H first and then T? P(H & then T) = 1 4

Fundamental Counting Principle If there are “m” ways that one event can occur and “n” ways that another event can occur, then there are (m x n) ways that both events can occur

Example A café’s lunch special is a hamburger meal. It comes with a choice of beverage (soda or tea) and a choice of salad (garden, potato, or bean). Create a tree diagram that shows the sample space.

Example A license plate consists of 2 letters followed by 3 digits. The letters, A-Z, and the numbers 0-9, can be repeated. Find the probability that your new license plate contains the initials of your first and last names in their proper order. Answer: 1/676 or 0.0015