Quiz Tomorrow!

Tomorrow we will start class with a 12 minute quiz! Come ready!

• What do I need to know for the quiz?

• Create a probability model for a given context
• Calculate expected value (show work)
• Calculate standard deviation and/or variance (using calc--1 Var Stats)
• Interpret expected value in a sentence

• How can I prepare for the quiz?

• Look over last night's multiple choice!
• Here is an answer key to last night's homework with ALL of the work shown:
• Random Variable MC KEY with Work (Click Me!)

• Look back at Monday night's homework and/or key (linked below) to review "interpret expected value." 

• Look back at our weekend book work!
• p. 381-383: 3, 5, 7, 15, 21

• Try more practice problems!
• p. 382: #6b, 17, 19, 22
• Do these on separate paper and grade yourself for +2 on your quiz
• Here are the answers to 6b and 22
• 6b.) Table: probability of 1 dart 0.1, prob for 2 darts = 0.09, prob. for 3 darts = 0.081, prob for 4 darts (and win) = 0.0729, prob for 4 darts (and lose) = 0.6561
• 6b.) E(# darts) = 3.44
• 6c.) E(wnnings) = $17.20
• 22a.) Table: prob. of 0 males = 0.143, prob. of 1 male = 0.571, prob. of 2 males = 0.286
• 22b.) E(# males) = 1.14 males
• 22c.) st. dev(# males) = 0.64 males

Tuesday HW = AP MC!

Tonight's homework gives us some more practice with expected value (and a lil' review in #6)! 

These questions represent some great preparation for the AP exam, for our upcoming test, and for the expected value "warmup quiz" we'll start class with on Thursday!

Here's the homework questions and a few tips/comments:

• AP MC Homework Tues 12/10 (Click Me!)
• Answer every question!
• Make notes/comments/show work to provide evidence that you actually worked hard on this and didn't just circle 7 answers!
• You should definitely be able to do 1, 2, and 5 fairly easily. Don't overthink them!
• We also have a stamp problem that was like #6 you can reference....
• Even if you aren't sure how to do a question or show the exact/correct work in its entirety, try to use some "multiple choice strategies" and come up with an answer!
• For example, #7 is the toughest question mathematically, but if you can't figure it out you can make an educated guess!
• On the AP exam you would want to complete these in about 18 minutes. Maybe time yourself for practice! (But then if you didn't finish go back and do the rest, don't show me any incomplete homework! Practicing the math is more important than practicing the timing tonight).
• I'll provide the answers and we'll go over any questions tomorrow in class.

Tomorrow we'll get back to "combining random variables" with the goal of finishing chapter 16 by the end of Friday! That'll leave us with 3 days to cover chapter 17 before our tests!

Monday's HW:

• Monday's HW: Understanding Expected Value (Click Me!)
• The key to this assignment is understanding how to calculate the probabilities for the table....
• Remember, we are going to play some game twice and look at the sum of the scores for each game; in any individual game we can score 0, 1, or 2 points....
• The table is giving us the sum of the points from two games; how could we earn a sum of 0? How many points would we need in the first game and then the second?
• Or, to get a sum of 3, we could get a "___ and ___," or a "___ and ___." 
• Use the probabilities shown in the graph and your "words and lines" to calculate the probability we get a sum of 0!
• Be sure to check that your probabilities add up to 1!

Always check your answers! Here's a key:

• Monday's HW: Uncovering Expected Value (ANSWER KEY, CLICK ME!)

Tomorrow it's on to more new stuff. See you there!

Weekend HW!

This weekend please complete the following in your textbook....

(*Note: this was changed/updated during period F Friday)

Weekend HW: p. 381-383 : 3/11, 5, 7, 15, 21

• This homework provides some key practice--be sure to do it thoroughly, check your answers, and more so, if you got something wrong go back and figure out your mistake!
• We have to move quickly to finish our unit before break, so it's important you get this practice on your own, as we won't have a ton of time to practice in class.
• For #3 you need to know about a deck of cards...
• There are 52 total cards
• There are 13 spades, 13 clubs, 13 hearts, and 13 diamonds (13 of each suit)
• There is one Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, for each suit
• So, there are 4 Aces, 4 2's, 4 3's, and so on...
• For 5ab you want to use a probability model for the number of children...
• But for 5c you want the expected number of boys, so you need a new model showing "# of boys" as your outcome rather than "# of children"
• For 11 and 15b:
• To find standard deviation we need to use our graphing calculator!
• Enter the outcomes in L1, probabilities in L2
• Go to STAT --> CALC --> 1 Var Stat
• XList = Outcomes (L1), FreqList = Probabilities (L2)
• Or, if you have an older model, when "1 Var Stat" pops up you need to type "1 Var Stat Outcome List, Probability List" or "1 Var Stat L1, L2."
• Standard deviation = sigma
• Expected value = mean 
• Do 15a and b both on the calculator!
• ALWAYS CHECK YOUR ANSWERS IN THE BACK OF THE BOOK. Then, if you got something wrong, go back and try to figure out the correct approach!

Want to get ahead? Here's Monday's HW:

• Feel free to do the work on separate paper; I'll give you copies of this Monday
• Monday's HW: Understanding Expected Value (Click Me!)

Thursday HW

This has been a crazy/disjointed week with the return from break (those days are always sluggish) and a surprise snow day...this means where a little behind where we want to be pacing wise, so come ready to work tomorrow and next week. Next Monday we really have to get back into the groove/routine; we've got 10.5 days of work before our next break, and we need to make the most of them. I know it's hard to stay motivated this time of year--it is for me too--but let's keep pushing each other and keep each other on top of our game.

You have two responsibilities to take care of tonight....

1.) Play with your laptop! Hopefully you're using it to check the blog right now! 

• Note: you won't need it in my class, so I guess it's up to you if you bring it to school. Check with your other AP teachers to see if you'll need it for them. 

2.) Do the extra credit homework! More practice = better preparation (and extra credit!)

• p. 363-366: 12, 24, 29, 33, 45
• 12 and 24 are similar to 11, 21, 23a shown a few blog posts below!
• For 29 try to use the independence formula....
• Does P(high BP) = P(high bp / high chol.)? That is, if we know someone has high cholesterol does it make them more/less likely to have high bp? 
• Or....
• Does P(high chol.) = P(high chol / high bp)? That is, if we know someone has high bp does it make them more/less likely to have high cholesterol?
• 33 = more independence formula
• Also, use the answers in the back of the book to help develop/strengthen your understanding for 29, 33
• Always check your answers/grade yourself for full credit! Here are 12, 24:
• 12a.) 0.62
• 12b.) 0.867
• 12c.) 0.194
• 12d.) 0.66
• *Note: b and c are conditional! And for d remember to pay attention to any overlap!
• 24a.) P(Canada given Mexico) = 0.444
• 24b.) No, going to Mexico and Canada are not disjoint; 4% of people have been to both.
• 24c.) P(Canada) = 0.19, and P(Canada/Mexico) = 0.444--Therefore, someone who has traveled to Mexico is more likely to go to Canada than a random person, so going to Canada/Mexico are not independent. 

Weds HW (**Changed from original plan**) + Vocab Quiz Tomorrow

**If you already did the textbook homework that was originally assigned for today you can do it for extra credit (due Friday)**

1.) For homework let's continue to work through the AP free response and AP multiple choice from class today....

• First, finish the 2 multiple choice, 2019 free response, and 2017 free response from class!
• The more time you put into figuring this stuff out, the better prepared you'll be! These are the types of questions we'll see on our unit test (and the AP exam)!
• Next, grade yourself! Use the info below to score each section as E, P, or I:
• 2019 Free Response:
• Part A:
• E: all 3 probabilities calculated correctly (with work shown for aii, aiii)
• P: 2 of 3 calculated correctly
• I: none or 1 of the 3 calculated correctly
• ai.) 0.0636
• aii.) 0.5864
• aiii.) 0.12
• Part B: 
• E: states independent, writes in context, supports using probabilities  from the table
• b.) Yes, the events of being a person whose response is never and being a woman ARE independent because P(N/W) = 0.12 = P(N) = 0.12.
• Here are some other mathematical approaches:
• Part C: 
• E: calculates correct probability of 4 or 5 will always take medicine 
• P: calculates probability of 5 taking medicine correctly, but fails to multiply by number of arrangements (5) for 4 people taking medicine
• c.) 0.24149
• Here's a link to the full scoring rubric:
• 2019 Scoring Rubric (scroll down to #3)
• 2017 Free Response:
• Part A:
• E: must satisfy the following 3 components:
• indicates normality and parameters (mean, st. dev)
• This can be done by labeling mu, sigma, and normalcdf, or by showing a sketch that identifies the mean in the middle and labels at least 1 st. dev. above or below (128 or 138)
• indicates boundary/direction
• This can be done by labeling "lower, upper" in a normalcdf calculation and/or by labeling the lower bound and shading the correct direction in a sketch
• calculates correct probability = 0.2119
• Part B:
• E: correct probability calculated AND supporting work is shown
• If tree diagram is used, show it, multiplication across branches is implied
• MUST show addition of values from tree
• P: correct answer, insufficient work (ie doesn't show the addition)
• P: switches probabilities for J, K in tree diagram but all other work is correct
• Answer = 0.4007
• Part C:
• E: correct probability calculated AND supporting work for conditional probability shown
• Answer = 0.3707
• Here's a link to the full scoring rubric:
• 2017 Scoring Rubric (scroll to question #3)
• 2 AP MC:
• 1.) B
• *Note: look at the quesiton--this is a conditional probabliity!
• 2.) D

2,) Chapter 15 Vocab Quiz Tomorrow!

• Much of the vocab on tomorrow's quiz repeats from our last (ch. 14) quiz, so use that to study!
• Equally likely events
• Disjoint/Mutually Exclusive
• Complement
• Sample Space
• Probability
• Law of Large Numbers
• Union
• Intersection
• Independent Events
• New (ch. 15) vocab)
• Conditional Probability
• Venn Diagram (when do we use it?)
• Tree Diagram (when do we use it?)
• Given 5 questions determine which do/do not require the use of conditional probability
• With replacement vs. without replacement

Monday/Tuesday

For those of you who were out today, in class we:

• Looked at a "universal" application of tree diagrams with medical testing (stamp)
• Notes/discussion:
• How do we determine if events are independent using probability?

Tomorrow in class we'll do some AP FR and AP MC (in groups). Then, Wednesday it's on to chapter 16!

**We will have our chapter 15 vocab quiz to start class on Wednesday.**

Monday Homework: p. 363-366: 12, 24, 29, 33, 45

• This assignment is due/will be checked Wednesday!
• 12 and 24 are similar to 11, 21, 23a shown in the blog post below!
• For 24c look at today's notes about "equations and displays"--there are two ways you can approach this....
• For 29 try to use the independence formula....
• Does P(high BP) = P(high bp / high chol.)? That is, if we know someone has high cholesterol does it make them more/less likely to have high bp? 
• Or....
• Does P(high chol.) = P(high chol / high bp)? That is, if we know someone has high bp does it make them more/less likely to have high cholesterol?
• 33 = more independence formula
• Also, use the answers in the back of the book to help develop/strengthen your understanding for 29, 33
• Always check your answers/grade yourself for full credit! Here are 12, 24:
• 12a.) 0.62
• 12b.) 0.867
• 12c.) 0.194
• 12d.) 0.66
• *Note: b and c are conditional! And for d remember to pay attention to any overlap!
• 24a.) P(Canada given Mexico) = 0.444
• 24b.) No, going to Mexico and Canada are not disjoint; 4% of people have been to both.
• 24c.) P(Canada) = 0.19, and P(Canada/Mexico) = 0.444--Therefore, someone who has traveled to Mexico is more likely to go to Canada than a random person, so going to Canada/Mexico are not independent. 

Chapter 15 Vocab List: Quiz Weds

• All words from our ch. 14 quiz are free game! Especially....
• Equally likely events
• Disjoint/Mutually Exclusive
• Complement
• Sample Space
• Probability
• Law of Large Numbers
• Union
• Intersection
• Conditional Probability
• Independent Events
• Venn Diagram (when do we use it?)
• Tree Diagram (when do we use it?)
• Given 5 questions determine which do/do not require the use of conditional probability
• With replacement vs. without replacement