SWBAT: - Identify the sample space of a probability experiment and simple events - Use the Fundamental Counting Principle to find the number of ways 2 or more events can occur - Distinguish among Classical, Empirical, and Subjective probabilities - Find the probability of the complement of an event - Use a tree diagram and the Fundamental Counting Principle to find more probabilities Agenda: - Notes - Homework

Probability - the likelihood that an event will occur Probability Experiment -A trial or experiment through which data is obtained, can be responses, counts and measurements Outcome - Result of a single trial in an experiment Sample Space - Set of all possible outcomes Event -A subset of a sample space that consists of one or more outcomes

Example: Probability Experiment: Draw a 10 from standard deck of cards Sample Space: {A,2,3,4,5,6,7,8,9,10,J,Q,K} Event: Select a 10 {10H, 10D, 10C, 10S} Outcome: You select a K : {K}

Tree Diagram -Used to find the number of possible outcomes of an experiment by using branches that originate at a starting point Possible outcomes for flipping 2 coins Possible outcomes for flipping 3 coins Simple Event Event that is made up of a single outcome Example: flipping 3 tails occurs only once

Example: Show the possible outcomes given you have 2 pairs of Shorts (blue & black), 3 t-shirts (white, green, yellow), and 2 pairs of shoes (sneakers or flip flops) Example: Show the combinations possible for a couple who want to have 4 children

Fundamental Counting Principle -If one event occurs m ways and another event occurs n ways, then the possible ways the events can occur in sequence is m*n Example: How many ways can you order a one topping pizza if they offer 3 different crusts, 2 sauces, and 8 different toppings 3 * 2 * 8 = 48 different choices for a one topping pizza Example: How many ways can you make a 5 digit number? 10 * 10 * 10 * 10 * 10 = 100,000 How many ways can you make it if it must start with 1 or 2? 2 * 10 * 10 * 10 * 10 = 20,000

In an individual bag of M&M's, the following info was observed: ColorFrequency Red7 Blue12 Green10 Brown6 Yellow7 Orange8 Find P(green) = Find P(red) =

Law of Large Numbers - the more an experiment is repeated, the more the empirical property of an event approaches the actual property of the event Subjective Probability - is based on an educated guess, expert opinion, and estimates Classify the type of probability for each statement The probability that the football team will win on Friday is 75%. Subjective The probability that student selected at random is a freshman is 29%. Emperical The probability of winning the raffle if 2500 tickets are sold. Classical

Range of Probability Rule 0 ≤ P(A) ≤ 1 [ | | | ] Impossible Unlikely Even Chance Likely Certain Complementary Events - the set of all outcomes in the sample space that are not included in the event, E' (E prime)

Homework Pg 138 # 8 – 72 every 4th