We Made it to Break!

**If you need to make up the probability math test (Weds 12/19) or vocab test (Thurs 12/21) you must do so within the first 3 days after break!**

Merry Christmas, Happy Holidays, Happy New Year, all that good stuff! Have an amazing week off! Spend lots of time enjoy your friends, family, some alone time, and some Statistics! Oh, and do this stuff too....

1.) Start reviewing for midterms over break!

• This exam is going to be tough (just like the AP exam)! If you want to do well (and you better want to do well!) you HAVE to prepare!
• Our midterm is a practice AP exam! ALL questions will be selected from past AP exams, and this will be an authentic opportunity to gauge how we might do in May!
• 60 minutes = 5 AP Free Response
• 60 minutes = 27-30 AP Multiple Choice
• How can I start studying for the midterm exam?
• We will have review stamps in class, but we will not dedicate any full class periods to review--it's your job to study as an AP student!
• Complete the review multiple choice practice test (sent via Remind, or you can email me for a copy)
• Create an outline of your notes--read through your notes, and as you do so, type up an outline!
• This will force you to review all concepts/vocab, and creating the outline will challenge you to determine what information is most important!
• Look over each of your past tests/quizzes for examples
• Do lots of practice problems!
• BEST OPTIONS TO REVIEW:
• 1.) Complete AP free response and use the rubrics to check your answers/score your responses!
• You can find EVERY released AP FR online, linked on the right...
• ..or just click me!
• 2.) Review by topic using the Khan Academy AP Stat course

2.) Winter Break Assignment = Teaching Yourself Ch. 13 (Experimental Design)

• You must email me for a copy of the assignment if you need it (too large to post as images on the blog)--carofano.fm@easthartford.org
• Here's your task...
1. Read chapter 13 and complete the "reading questions" provided--these may be collected and graded for (thorough) completion (classwork grade)
• Your responses to these questions serve as your notes for experimental design!
• The bold words are our vocab for this chapter
• The more thoroughly you complete these questions and the more effort you put into this, the more prepared you'll be! This stuff will be on our midterm!
• You can record all answers on the paper provided, or you can put this all in your notes
• Extra Credit Stamp Opportunity: on separate paper write down any questions you have about the content you read! You must write a complete sentence/question. For example...
• "What does it mean if we use blocking in an experiment?"
• NOT..."blocking..." (that's not a question)
• We WILL NOT review all of chapter 13 in class, but your questions will help me to determine exactly what content we should go over in our limited time before exams....
2. Complete the 19 multiple choice questions based on your reading/notes--this will be collected and graded as a quiz the day we return

Thursday (Almost There!)

**If you were out yesterday or today you must make up your math and/or vocab test tomorrow during school (I am leaving right at 2:10)!**

There is no homework tonight! But there is work over break....

1.) Start reviewing for midterms over break!

• This exam is going to be tough (just like the AP exam)! If you want to do well (and you better want to do well!) you HAVE to prepare!
• Our midterm is a practice AP exam! ALL questions will be selected from past AP exams, and this will be an authentic opportunity to gauge how we might do in May!
• 60 minutes = 5 AP Free Response
• 60 minutes = 27-30 AP Multiple Choice
• How can I start studying for the midterm exam?
• We will have review stamps in class, but we will not dedicate any full class periods to review--it's your job to study as an AP student!
• Complete the review multiple choice practice test (sent via Remind, or you can email me for a copy)
• Create an outline of your notes--read through your notes, and as you do so, type up an outline!
• This will force you to review all concepts/vocab, and creating the outline will challenge you to determine what information is most important!
• Look over each of your past tests/quizzes for examples
• Do lots of practice problems!
• BEST OPTIONS TO REVIEW:
• 1.) Complete AP free response and use the rubrics to check your answers/score your responses!
• You can find EVERY released AP FR online, linked on the right...
• ..or just click me!
• 2.) Review by topic using the Khan Academy AP Stat course

2.) Winter Break Assignment = Teaching Yourself Ch. 13 (Experimental Design)

• You must email me for a copy of the assignment if you need it (too large to post as images on the blog)--carofano.fm@easthartford.org
• Here's your task...
1. Read chapter 13 and complete the "reading questions" provided--these may be collected and graded for (thorough) completion (classwork grade)
• Your responses to these questions serve as your notes for experimental design!
• The bold words are our vocab for this chapter
• The more thoroughly you complete these questions and the more effort you put into this, the more prepared you'll be! This stuff will be on our midterm!
• You can record all answers on the paper provided, or you can put this all in your notes
• Extra Credit Stamp Opportunity: on separate paper write down any questions you have about the content you read! You must write a complete sentence/question. For example...
• "What does it mean if we use blocking in an experiment?"
• NOT..."blocking..." (that's not a question)
• We WILL NOT review all of chapter 13 in class, but your questions will help me to determine exactly what content we should go over in our limited time before exams....
2. Complete the 19 multiple choice questions based on your reading/notes--this will be collected and graded as a quiz the day we return

Here's the plan leading up to midterms: I made some changes to my original plan (after period A on Thursday), so we'll be doing something a little weird--move on to next unit, then back to probability, then back to new unit....

• Wednesday (12/19): Chapter 14-16 Probability Test
• Thursday (12/20): Chapter 14-16 Vocab Test
• Friday (12/21): Intro to Next Unit --> Outlining the Statistical Process
• Wednesday (1/2) to Friday (1/4): Notes on experimental design (take home quiz over weekend)
• Monday (1/7): chapter 13 (experimental design) wrap up 
• Tuesday (1/8) to Friday (1/11): Back to probability--chapter 17 notes (binomial v. geometric probability)

STUDY AGAIN!

Tomorrow we have round two--our probability vocab test, and there will also be 2 math problems mixed in (yay)! You will have 25 minutes to complete this test!

Again, STUDY, STUDY, STUDY! We HAVE to ace these vocab tests--it's all about preparation.

Use your chapter 14, 15, and 16 quizzes to review (I gave you the ch. 16 vocab quiz in class today); make a quizlet, make flashcards, whatever works--but come ready!

Probability Vocabulary List:

• Probability
• Law of Averages
• Law of Large Numbers
• Equally Likely
• Sample Space
• Complement
• Independent (Events)
• Mutually Exclusive aka Disjoint (Events)
• Union
• Intersection
• Venn Diagram
• Tree Diagram
• Conditional Probability
• Random Variable
• Probability Model
• Expected Value
• Variance
• Standard Deviation 
• Discrete Random Variable
• Continuous Random Variable
• Shifting
• Rescaling
• Pythagorean Theorem of Statistics

What else is (or could be) on the vocab test?

• Determine if given events are disjoint, independent, neither, or both (never both!)
• Determine if a given question requires conditional probability or not
• Interpret expected value
• Shifting/Rescaling Stuff
• 2 more math problems...surprise!

Chapter 16 Vocab Quiz Key:

1. D
2. E
3. B
4. E
5. C
6. B
7. D
8. A
9. B
10. D
11. A
12. A
13. B

After tomorrow's test we will start our last chapter of probability (chapter 17: binomial and geometric probability)! We'll continue with this Friday, and then for the three days after break! See you there!

Here's the plan for the rest of the unit (and what happened today):

• Wednesday (12/19): Chapter 14-16 Probability Test
• Thursday (12/20): Chapter 14-16 Vocab Test (20 min), then Chapter 17 intro notes
• Friday (12/21): More Chapter 17 Notes (binomial and geometric probability)
• Wednesday (1/2) to Friday (1/4): Finish probability unit (chapter 17) with ANOTHER "mini test" on probability....
• There will be a take home assignment over break! It will either be....
• Take Home Test (review of everything!)
• "Teaching Yourself Chapter 13" Assignment

Test Tomorrow!

Tomorrow's Test = all of probability (chapters 14-16)!

Tonight you have one responsibility: STUDY, STUDY, STUDY!

1.) Look over your notes, read through examples!
2.) Look over your past quizzes and/or homework!
3.) Complete ALL of the practice problems provided in class today! (answers below)

• If you were absent today email me (carofano.fm@easthartford.org) and I will send you all of the attachments--it's too much to post on the blog as images

Check your answers below!

If you can't figure something out, send me a Remind message! We can converse to try to figure it out, and at worst, I can send you a picture with all of the work shown!

Probability Chapter 15 Quiz! KEY

• 1a.) 0.44
• 1b.) 0.12
• 1c.) 0.56
• 1d.) 0.586
• 2a.) 0.1022
• 2b.) 0.8978
• 2c.) 0.1166
• 3a.) 0.716
• 3b.) 0.014
• 3c.) 0.042
• 3d.) 0.951
• 3e.) 0.02
• Bonus: 0.7599

Combining Random Variables AP MC! KEY

1. D
2. 0.1204
3. C
4. B
5. B
6. E
7. C
8. D
9. D

Review Multiple Choice (Mixed Practice) KEY

1. D
2. D
3. A
4. A
5. D
6. A
7. C
8. B
9. C
10. D
• For #10: There are 56 different ways to arrange 3 "in" among 8 serves--I would not make you figure out such a large number of arrangements (yet), so the important thing here is more the idea than figuring out the 56
11. E
12. B
13. A
14. D
15. A
16. E
17. D

Good luck! email/Remind me with any questions! See you all tomorrow for the big day!

Monday, Monday, Monday!

Monday's HW (these questions are also on the worksheet provided in class, or below):

Page 383-384: 33, 37, 38 

• Check out the "Step by Step: Packaging Stereos" example on pages 376-378 for an example of these types of problems!
• 
• Homework Answer Key:
• 33a.) 1 oz
• 33b.) 0.5 oz
• 33c.) 0.023
• 33d.) Mean = 4 oz, St. Dev. = 0.5 oz
• 33e.) 0.159
• 33f.) Mean = 12.3 oz, St. Dev. = 0.54 oz

• 37a.) Mean = 200.57 sec, St. Dev. = 0.46 sec
• 37b.) No, the team is not likely to swim faster than this; the probability of the team beating this time is 0.009. 

• 38a.) Mean = 37.6 min, St. Dev. = 3.7 min
• 38b.) No, I do not think the bike will be ready/set up as promised; the probability of this happening is only 0.02, or a 2% chance. 

Here's the plan for the rest of the unit (and what happened today):

• Monday (12/17): Chapter 16 Notes/Practice: More Combining Random Variables and applying the Normal Model
• Stamp = Review for Test!
• HW Q's
• Notes = last 2 slides (wait times and stereos)
• We did not get to question 2 for the stereo example
• Get these notes from a classmate!
• Tuesday (12/18): Chapter 14-16 Wrap Up, Questions, Practice
• Wednesday (12/19): Chapter 14-16 Probability Test
• Thursday (12/20): Chapter 14-16 Vocab Test (20 min), then Chapter 17 intro notes
• Friday (12/21): More Chapter 17 Notes (binomial and geometric probability)
• There will be a take home assignment over break! It will either be....
• Take Home Test (review of everything!)
• "Teaching Yourself Chapter 13" Assignment

Weekend HW

This weekend please complete the following in your textbook:

Page 382-384: 6, 23, 27ab, 31bc, 33abd

• Use today's notes and the Pythagorean Theorem of Statistics (VARIANCES ALWAYS ADD!) with 23, 27, 31, and 33
• For 23 you are practicing your "shifting/rescaling" and "combining random variables" skills...
• For example, "3X" would mean we're multiplying each outcome for variable X by 3--your job is to find the new mean and standard deviation
• If a question says "X1 + X2," this means we're adding these two random variables, and need to find the mean and standard deviation based on today's notes
• For #6 we assume that a person will stop playing if/when they win the prize
• *For 6b and 6c you'll need two different probability models--part (a) is asking you to create these...
• 6b asks for the expected number of darts thrown, so we need a model with the "outcomes" as "# of darts thrown"
• 6c asks for the expected winnings, so we need a model for the "winnings
• Answers to #6:
• 6a.) # darts = 1, 2, 3, 4; probabilities = 0.10, 0.09, 0.081, 0.729
• 6a.) amount won = $95, $90, $85, $80, $-20; probabilities = 0.10, 0.09, 0.081, 0.073, 0.656
• 6b.) 3.44 darts (use the model for the # darts thrown)
• 6c.) $17.20 (use the model for the amount won) 

Monday's HW (these questions are also on the worksheet you took in class):

Page 383-384: 33, 37, 38 

• On Monday we'll extend our thinking and start to apply the Normal model...
• These questions require us to use what we learned today to find a new mean and standard deviation (after we combine random variables), and then apply the Normal model!
• Feel free to try to figure these out and get a head start on Monday's hw! You got this
• Check out the "Step by Step: Packaging Stereos" example on pages 376-378 for an example of these types of problems!

Here's the plan for the rest of the unit(and what happened today):

• Friday (12/14): Chapter 16 Notes/Examples: Combining Random Variables
• Stamp = Shifting Rescaling Practice (question below--do this if you were out!)
• Each outcome for a random variable has been transformed by multiplying by 5 and then subtracting 10. If the original probability model resulted in an expected value of 8 and a variance of 9, what are the expected value and variance after the transformation?
• Vocab: Discrete v. Continuous Random Variables
• Pythagorean Theorem of Statistics!
• Looked at how we combine random variables -- we used our "middle right slide" about the costs of vet visits for cats and dogs! (get these notes from a classmate)
• Monday (12/17): Chapter 16 Notes/Practice: More Combining Random Variables and applying the Normal Model
• Tuesday (12/18): Chapter 14-16 Wrap Up, Questions, Practice
• Wednesday (12/19): Chapter 14-16 Probability Test
• Thursday (12/20): Chapter 14-16 Vocab Test (20 min), then Chapter 17 intro notes
• Friday (12/21): More Chapter 17 Notes (binomial and geometric probability)
• There will be a take home assignment over break! It will either be....
• Take Home Test (review of everything!)
• "Teaching Yourself Chapter 13" Assignment

Thursday HW:

Tonight please complete the two questions below for homework:

1.) "Middle left slide" for chapter 16 (feel free to glue this in and do it in your notes!)

• Note: pay attention to the fact that we're given variance and asked for variance....but everything we learned about shifting/rescaling applies to standard deviation!
• So, first, find the original standard deviation from the variance...
• Then find the "new" standard deviation for each bullet...
• Finally, convert this standard deviation back to a variance
• You cannot apply the rules of shifting/rescaling directly to variance!

2.) Complete #19 on page 382 (or below):

Tomorrow in class we'll continue to move forward and start to learn about the last component of chapter 16, "combining random variables."

Here's the plan for the rest of the week (and what happened today):

• Thursday (12/13): Chapter 16 Notes/Examples: Combining Random Variables
• Stamp = 4 MC on the back of yesterday's pinata classwork
• HW Questions
• New Stuff: Shifting and Rescaling Random Variables
• Example for Notes:
• Context: Pinball Wizard: Expected Prize Amount = $7.34, St. Dev. = $136.05
• Question 1: If each (original) prize amount were cut in half, what would the new expected value and standard deviation of prize amounts be?
• How could we find these using our calculator?
• Using the "rules" of shifting/rescaling?
• Question 2: If each (original) prize were increased by $5, what would the new expected value and standard deviation of prize amounts be? 
• How could we find these using our calculator?
• Using the "rules" of shifting/rescaling?
• Friday (12/14): Chapter 16 Notes/Examples: Combining Random Variables
• Pythagorean Theorem of Statistics!
• Monday (12/17): Chapter 16 Notes/Practice: More Combining Random Variables
• Tuesday (12/18): Chapter 14-16 Wrap Up, Questions, Practice
• Wednesday (12/19): Chapter 14-16 Probability Test
• Thursday (12/20): Chapter 14-16 Vocab Test (20 min), then Chapter 17 intro notes
• Friday (12/21): More Chapter 17 Notes (binomial and geometric probability)
• There will be a take home assignment over break! It will either be....
• Take Home Test (review of everything!)
• "Teaching Yourself Chapter 13" Assignment

Wednesday HW

Tonight please complete the "Uncovering Expected Value" worksheet provided in class (or below).

• This assignment gets us thinking about how we might develop a casino game and determine what to charge people and/or what prizes we might assign!
• The hardest part may be calculating the probabilities for the probability model (#1)....
• Remember, we are going to play a game twice...
• Each time we play the game we can earn 0, 1 or 2 points (in one play)
• The "outcomes" in the table are the "sums," or how many points we earn (total) in the two games combined
• Think: how could we have a sum of, say, 3? 
• How many points would we get on the first play? And on the second?
• Or, what's another way--what could we get on the first? And on the second?
• Here are the correct probabilities for your model so you can check, and/or so you can use these to complete the rest of the assignment. 
• (of course you have to figure out how to find all of these):
• P(sum = 0): 0.16
• P(sum = 1): 0.24
• P(sum = 2): 0.33
• P(sum = 3): 0.18
• P(sum = 4): 0.09
• For #5 you should get an expected value of $153 if you allot the prize amounts correctly
• On the back:
• These are the same sums from the front, so the probabilities are the same...
• Now we want to think about making this a gambling game--your job is to decide which prize amount goes with which sum.....

Tomorrow in class we'll move on to the second half of chapter 16--combining random variables! See you there!

Here's the plan for the rest of the week (and what happened today):

• Wednesday (12/12)
• Stamp: Pinball Wizard
• Practice finding expected value and standard deviation with calculator
• Interpreting and using expected value
• HW Questions
• Classwork: Pinata Free Response (more practice!)
• Thursday (12/13): Chapter 16 Notes/Examples: Combining Random Variables
• Friday (12/14): Chapter 16 Notes/Examples: Combining Random Variables
• Monday (12/17): Chapter 16 Wrap-Up Notes/Practice: Combining Random Variables
• Tuesday (12/18): Chapter 14-16 Review, Questions, Practice
• Wednesday (12/19): Chapter 14-16 Probability Test
• Thursday (12/20): Chapter 14-16 Vocab Test (20 min), then Chapter 17 notes
• Friday (12/21): More Chapter 17 Notes
• There will be a take home assignment over break! It will either be....
• Take Home Test (review of everything!)
• "Teaching Yourself Chapter 13" Assignment

2's Day HW

We may or may not start class with a quiz tomorrow...I can't make up my mind. I guess it'll be a surprise when you come in!

If we do have a quiz it will be based on chapters 14/15--the best thing to use to review is our weekend homework (ch. 14/15 review questions)! Tonight's homework and extra credit stamp would also help to review for that...

Tonight's Homework:

1.) Complete questions 3/11, 5/13, 7, 15, and 21 on page 381-383 (or on the handout provided in class)

• Homework Answers:
• 3a.) Amounts Won = 0, 5, 10, 30; Probabilities = 26/52, 13/52, 12/52, 1/52 (respectively)
• 3b.) $4.13
• 3c.) Less than $4.13 
• 11.) $5.44 (from calculator)
• 5a.) # Children = 1, 2, 3; Probabilities = 0.5, 0.25, 0.25 (respectively)
• 5b.) 1.75 children
• 5c.) 0.87 boys
• 13.) 0.83
• 7.) $27,000
• 15a.) 1.7
• 15b.) 0.9
• 21a.) # Good = 0, 1, 2; Probabilities = 0.067, 0.467, 0.467
• 21b.) 1.40
• 21c.) 0.61

2.) Extra Stamp Opportunity (3 possible stamps): DUE TOMORROW

• Glue the "Secret Santa" slide (bottom left one if you have it) to a piece of paper and answer questions 1-3
• If you lost your slide you can copy the question onto paper and answer 1-3
• Show all work
• Remember, after we draw a name for this secret santa we DO NOT put it back....
• Here's the question:
• 
  

Monday = Study Vocab!

Tonight please complete the following:

1.) STUDY! Chapter 14/15 vocab quiz to start class tomorrow

2.) Start getting ready for a math quiz (Wednesday)

• Look over the answer key from the "textbook homework" (Thursday night)
• Check all answers from the "weekend homework" (Ch. 14/15 review questions) and see where you stand/what you need help with

3.) Extra Stamp Opportunity (3 possible stamps): DUE WEDS

• Glue the "Secret Santa" slide (bottom left one if you have it) to a piece of paper and answer questions 1-3
• If you lost your slide you can copy the question onto paper and answer 1-3
• Show all work
• Remember, after we draw a name for this secret santa we DO NOT put it back....
• Here's the question:
• 
  

Here is the vocab list for tomorrow's quiz--the majority of these words repeat from our last vocab quiz:

• Sample Space
• Probability
• Complement (of an event)
• Disjoint or Mutually Exclusive Events
• Independent Events
• Probabilities of all possible outcomes sum to....
• Union 
• Intersection
• Equally Likely (Events)
• Conditional Probability--when do we use it?
• Venn Diagram--when do we use them?
• Tree Diagram--when do we use them?
• Recognize conditional--given 5 questions, identify which one does or does not require conditional probability (like our Titanic stamp)

And here is the answer key (with all work shown) for our weekend homework:

Tomorrow it's back to random variables, expected value, and probability models--see you there! 

Thursday AND Friday (Long Post)

**You have until the end of the day Monday (I will be here after school) to do the chapter 14 quiz retake if you like**

I will most likely be out tomorrow! Be sure to stay focused and ace your work--it will be collected and graded by the sub! Here's the plan....

• Complete the two AP free response and the AP multiple choice provided by the sub
• You can work in groups and use your notes--be motivated by learning more than the grade--take this as an opportunity to practice and strengthen your probability skills!
• We will have a chapter 15 quiz (vocab and math) in class on Tuesday! This classwork is a great way to start our prep for that quiz!

Thursday's HW: "Textbook Problems" Worksheet (or find them in the textbook)

• Be sure to check your answers in the image below (in red)
• If I am absent tomorrow I will check this Monday (and we'll discuss any questions)...
• For #43...
• Think: what's the "right decision" if someone was drinking? To detain the driver or to release them?
• What's the "right decision" if someone was not drinking? To detain them or release them?
• In your tree diagram for this question your first set of branches is "drinking or not drinking..."
• Your next set of branches will be "detain or release," and you have to connect these to the idea of "the right decision" to figure out what probabilities go where...

Weekend/Monday HW:

• Tomorrow the sub will give you a worksheet with chapter 14 and 15 "probability review questions..."
• Complete these to prepare for Tuesday's quiz! 
• All answers are given in parentheses--always check your work
• 
  
• 

On Monday in class we will finish our chapter 15 notes/slides (20 min); then, we'll start chapter 16! See you there!

**We will have a probability unit test after we finish chapter 16! The goal is....

• Probability "Math Test" = Wednesday (12/19)
• Probability Vocab Test = Thursday (12/20) --- 25 minute limit
• Then we'll discuss binomial and geometric probabilities after our vocab test and on Friday (12/21)

When's Day HW

Tonight please complete the tree diagram practice provided in class (or below)--one is about binge drinking, the other is about the type of high school students attended and their chances of graduating college.

• For the "binge drinking' question....
• The first information is defining binge drinking (5 or more drinks in a row for men, 4 ore more in a row for women)--these aren't probabilities, so these won't be used in our tree diagram....
• There are three "types of drinkers" defined, but only two probabilities for being involved in an alcohol related accident....
• Remember, those who drink moderately and those who abstain both fall into the category of "nonbingers..."
• For the private college question....
• The 70% refers to the percent of incoming freshmen (at this college) who attended a public high school
• Then, the chance of graduation is referring to the probability students graduate from this college depending on the type of high school they attended....
• Answer Key:
• You will receive a detailed key with all work shown tomorrow in class
• Binge Drinking:
• 1.) 0.1252
• 2.) 0.0748
• 3.) 0.0171
• 4.) 0.5974
• 5.) 0.4175
• Private College
• a.) 0.795
• b.) 0.75
• c.) 0.90
• d.) 0.6604
• e.) 0.1463
• f.) No....incoming freshmen who attended a private high school are more likely to graduate (90% chance) than incoming freshmen who attended a public high school (75% chance).
• Questions (in case you lost yours or were out)....

Tomorrow's (Thursday) HW: This is all based on the same type of stuff as tonight's homework (which we'll also practice tomorrow in class), so feel free to get a head start! These problems are all selected from the textbook....

Today's Class Recap:

• Stamp = practice identifying conditional probability
• HW Questions (book and worksheet)
• New Stuff: Using Tree Diagrams (and conditional probability)
• Completed the "middle right slide" example (about going to Canada and Mexico) using conditional probability
• Our homework tonight is also based on these ideas
• Here are the notes/example from class today:
• 

Two's Day HW

Tonight please complete the following: (you can find all of the homework questions and answers below, so you won't need a book tonight...)

1.) "Stamp" worksheet about "A school plans to create a committee of 4 students..." provided in class or below.

2.) (You can do these on the back of the worksheet if you like):

Page 364-365: 21ab, 22ab, 23

Here are the homework questions:

And here are the answers so you can check:

• "Stamp" Worksheet (A committee.....)
• a.) 0.0529
• b.) 0.956
• c.) 0.00882
• Textbook Problems page 364-365:
• 21a.) 0.32
• 21b.) 0.135

• 22a.) 0.25
• 22b.) 0.875

• 23a.) 0.266
• 23b.) No, having a garage and a pool are not independent because a house with a garage is more likely to have a pool (26.6%) than any random house (21%).
• 23c.) Having a garage and a pool are not mutually exclusive (disjoint) because some (17%) of homes have both. 

Today's Class Recap:

• Stamp = conditional probability and two way tables
• We then went over this problem in our notes and used it to develop a formula for conditional probability
• HW Questions (from book)
• Completed the "middle left slide" example (about going to Canada and Mexico) using conditional probability

Here's the plan for the coming weeks, in case you're curious:

• Wednesday (12/5): Notes/examples--conditional probability and tree diagrams
• Thursday (12/6): Chapter 15 Classwork/Practice
• Friday (12/7): Chapter 15 wrap up notes/practice
• Weekend = Ch. 15 take home quiz?
• Monday (12/10): Ch. 15 math quiz? Start ch. 16 notes
• Tuesday (12/11): Ch. 15 Vocab Quiz, Ch. 16 Notes
• Wednesday-Friday (12/12 to 12/14): Chapter 16 notes and classwork
• Monday (12/17): Chapter 16 wrap-up
• Tuesday (12/18): Probability Practice?
• Wednesday (12/19): Probability Math Exam
• Thursday (12/20): Probability Vocab Exam + Chapter 17 Intro
• Friday (12/21): Chapter 17 Notes/Examples
• We will finish chapter 17 and have a quiz after break
• Monday (12/24) to Tuesday (1/1) = Break
• You WILL have an assignment over break....either....
• Review Take Home (will be provided even if not assigned for practice)
• Chapter 13 Reading Questions/Quiz
• Wednesday (1/2) to Friday (1/4): Finish ch. 17 (end of probability)
• Monday (1/7) to Friday (1/11): Chapter 12 or 13 Notes
• Monday (1/14) to Friday (1/18): MIDTERM EXAMS = PRACTICE AP EXAM

Bonus Stamp Solution:

• Check out the solution (below) to the bonus stamp question we had over break--even if you didn't do it! 
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**You have a rare opportunity (for our class)--you can re-take a different version of the probability "math quiz!" **

• However, your re-take score will replace your first score even if it's a lower score...
• ...so don't just show up and wing the retake! You must study and come prepared--re-do the quiz you got back today!
• You must re-take the second version by 2:10 on Friday, during lunch, study hall, before school, or after school (Weds/Thurs).

Monday's Homework:

Page 362-365: 4, 9, 11, 17

• #9 is only in orange because it wasn't listed in the weekend post, the other three were
• For #9 and #17 you need to know how a deck of cards is made up...here you go:
• Standard Deck of Cards;
• 52 total cards
• 26 red cards
• 13 red cards are "hearts"
• 13 red cards are "diamonds"
• 26 black cards
• 13 black cards are "spades"
• 13 black cards are "clubs"
• Each of the suits (spades, clubs, hearts, diamonds) has 13 cards...
• 2, 3, 4, 5, 6, 7, 8, 9
• Jack, Queen, King, Ace
• So, there are four two's in a deck--a 2 of hearts, 2 of diamonds, 2 of spades, 2 of clubs
• There are four three's in a deck--3 of hearts, 3 of diamonds, 3 of spades, 3 of clubs
• Etc...
• #4 Answer Key:
• 4a.) 0.14
• 4b.) 0.23
• 4c.) 0.77

Today's Class Recap:

• Stamp = working without replacement (like #19 from the weekend homework)
• We then went over this problem (about marbles) in our notes
• HW Questions: Ind, Disjoint MC and book problems
• Independent/Disjoint MC Answer Key:
• 1.) E
• 2.) C
• 3.) E
• 4.) B
• 5.) A
• 6.) A
• 7.) C
• 8.) B
• 9.) C
• 10.) A
• 11.) A
• 12.) C
• 13.) B
• Then we started our next note slide and began a discussion of conditional probability (to be continued tomorrow)...

Bonus Stamp Solution:

• Check out the solution (below) to the bonus stamp question we had over break--even if you didn't do it! 
•