Warm-Up 1/31 1. Samantha gets a 4% raise at the end of the year. Suppose Samantha makes $48,000 this year. What will be her salary next year? Show two different ways on how to calculate this. 2. Your lawnmower runs on an oil to gas mixture of 1/6 to 4. If you buy a 24oz container of oil and use 1/6 of it. How much gasoline will you need?   How big of a container will you need to mix everything together?

Questions on Homework, due Quiz Thursday

Warm-Up Get into Pairs of 2 Get a worksheet from front table Challenge Connect the dots Play for 15 minutes

Warm-Up 1/29 You have a half sheet at your table, read directions and do the problem, tree diagram on the front area model on the back Discuss honors assignment Questions on next part – look at notes online Questions on Indep and Depend worksheet Make sure you subtract from Num and Denom in dependant Expected Value

Warm-Up New Seat Warm-up grab CMAS sheet on front table (coming soon)

Warm-up Take a CMAS practice sheet from front table Also take a Ind and Dep worksheet

Warm-Up 1/23 Given the point (-4,3) and slope = ¼ What is the equation in point slope form What is the equation in slope intercept from What are the x and y intercepts Given the line y=-2/3x+5 What is the equation of the line parallel and through the point (6,2) What is the equation of the line perpendicular and through the point (6,2)

Warm-Up 1/28 Take CMAS worksheet from front table This week Independent and Dependent probability Compound probability – multiply each event Expected Value Quiz Thursday IXL Due Friday

Warm Up

Likelihood something will happen Probability Likelihood something will happen Can’t be negative because we can’t have a negative number or outcomes or want a negative amount of something to happen

Probability

Homework Worksheet packet on Probability

Vocab Counting Principle how many different outcomes there could be Factorial Multiplication from one number down to 1 Permutation number of outcomes where order does matter Combination Number of outcomes where order doesn’t matter Sample Space how many outcomes there could be for an event or experiment Events Subset of a sample space, what you want to happen

Vocab Experimental using the results from an experiment to find probability Theoretical more of the mathematical probability something will happen Odds Another way to discuss likelihood Independent Event one event doesn’t affect another Dependent Event One event does affect another Expected Value

Counting Principle When there are m ways to do one thing and n ways to do another then there are m times n ways of doing both That gives you the total number of outcomes possible How many different ways to make a lunch if you have multiple choices to make your lunch 3 types of sandwiches, 2 different fruits, 3 different deserts 3*2*2=12 different lunches you can make

Combinations and Permutations Help to get the total number of outcomes for a specific event that happens Does order matter for the following A race Numbers pulled for a lottery Groups in a class room

Perm and Comb P stands for permutation n total r what you want C stands for combination – the extra r in the denom accounts for the repeats

Example

Experimental and Theoretical Probability Depending on what is given finding the probability

Examples

Example

Odds another way to discuss likelihood

Example

Probability Tree and Area Diagrams These are ways to help organize and visualize outcomes and each probability Tree – each branch represents one event with multiple events you multiply along a path add all the paths down and should give you 100% Area diagrams used when 2 events happening One event on top and one event on left side Multiply to get values inside the boxes All should add to 100%

Example Draw a probability tree that represents flipping a coin 3 times Draw a probability tree that represents picking two marbles from a bag containing 3 red, 2 blue and 5 yellow What are things you notice How does this help

Warm - Up Based on our notes yesterday make a probability tree and an area diagram for the following experiment You spin the following spinner and you roll a die. After you make the diagrams answer the following questions What is the probability of getting the same number on the spinner and die What is the probability the numbers are both multiples of 2

Honors Work Substitution idea is to solve one equation for a variable and substitute it into the other one Elimination get the coefficient of one variable to be opposites so when you add them together they cancel out Word Problems y = mx + b is what we have done we look for the slope or per and the starting place or constant b

Word Problems Ax + By = C x and y are going to represent the information in the word problem A and B are things that you do to the information in the work problem C is the total Adam has dimes and quarters in his pocket. There are 28 coins in all and they are worth $4.60 altogether. How many quarters does Adam have. X and y represent the number of dimes and quarter We know they total 19 and we know how much dimes are quarters are worth X + y = 19 .1x + .25y = 4.6

Homework Good – some difficulty with the odds Quiz – still a little understanding with the Perm and Comb

Independent and Dependent Probability Usually use the terms with and without replacement You have a bag full of marbles different colors You take a marble out and keep it out now the next event has a different number of marbles You roll a die and flip a coin, one doesn’t have any affect on another You pick a marble and put it back, same number of marbles still in the bag

Example Roll a die Twice What is the probability of rolling a 3 the first time and a 2 the second time? P(A and B) = P(A)*P(B) Selecting a marble from a bag and replacing it and then selecting another one. The bag contains 2 red, 1 white and 7 yellow. What is probability of selecting a white and then a yellow marble

Example A class has 18 boys and 12 girls. Two students are chosen at random. What is the probability that the students chosen will be a boy and a girl. P(A and B) = P(A)*P(B after A)

Expected Value This helps to determine if a game is fair It helps to calculate what the average is for each term

Free Throws

Problem 4.3 Work in your groups on problem 4.3 You can skip 3 and 4 under A We need the basics to help understand expected value

Expected Value Take sheet from front 4.4 Work as a group and go through the process Need data from previous problem

One-and –One Expected value Nishi takes 100 shots How many times do you expect her to get 0 points? How many times do you expect her to get 1 point? How many times do you expect her to get 2 points? What is the total number of points she could score? Find the average number of points You just calculated the expected value

Calculating expected value Find probability of each situation Multiply each situation by the number of times they play Multiply each situation by the number of points Find the average Another way Find each persons probability Multiply each persons probability to the number of times they play Multiply answer from 2 to how much they make Subtract what the other person makes (this is what they pay out) Divide answer by number of times played to get the average

More in depth Problem If we play the game 100 times what is the expected value Prob Played Won Win Total Win Minus Payed Ave Al ¼ 100 25 4 100 100-75=25 25/100=.25 Betty ¾ 100 75 1 75 75-100=-25 -25/100=-.25

I pay you $6 when you hit gray and you pay me $8 when I hit white. Do you think the game is fair? Why? Find the expected value for each of us Prob Played Win Points Total Win-Pay Average You 8/15 30 16 6 96 -16 - 8/15 -0.53333 Me 7/15 14 8 112 0.533333